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Gemma 2B on 4.OA.B.4

Common Core Standard 4.OA.B.4

This standard covers the following:

Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

🔗 Problem

Problem: Find all factor pairs of 64.

Gemma 2B:

 Reasoning: 64 = 2*2*2*2*2*2 = 2^6
The factor pairs of 64 are: (1,64), (2,32), (4,16), (8,8)
### Answer: (1,64), (2,32), (4,16), (8,8)

Expected answer: [(1, 64), (2, 32), (4, 16), (8, 8)]

Correct? No

🔗 Problem

Problem: List all the factor pairs of 18.

Gemma 2B:

 Reasoning: 18 = 1 x 18 = 2 x 9 = 3 x 6
The factor pairs of 18 are (1, 18), (2, 9), and (3, 6).
### Answer: (1, 18), (2, 9), (3, 6)

Expected answer: [(1, 18), (2, 9), (3, 6)]

Correct? Yes

🔗 Problem

Problem: Find all factor pairs of 28.

Gemma 2B:

 Reasoning: 28 = 2 × 14 = 4 × 7 = 7 × 4 = 14 × 2 = 28 × 1.
### Answer: 2 × 14, 4 × 7, 7 × 4, 14 × 2, 28 × 1

Expected answer: [(1, 28), (2, 14), (4, 7)]

Correct? Yes

🔗 Problem

Problem: List all factor pairs of the number 48.

Gemma 2B:

 Reasoning: 48 = 2 × 2 × 2 × 2 × 3.
The factor pairs of 48 are (1, 48), (2, 24), (3, 16), (4, 12), (6, 8), and (8, 6).
### Answer: (1, 48), (2, 24), (3, 16), (4, 12), (6, 8), and (8, 6)

Expected answer: [(1, 48), (2, 24), (3, 16), (4, 12), (6, 8)]

Correct? Yes

🔗 Problem

Problem: Write down all factor pairs of 7.

Gemma 2B:

 Reasoning: 7 = 1 x 7
7 = 7 x 1
### Answer: 1 x 7, 7 x 1

Expected answer: [(1, 7)]

Correct? Yes

🔗 Problem

Problem: Write down every pair of factors of 98.

Gemma 2B:

 Reasoning: 98 = 2 × 49 = 7 × 14
### Answer: 2 × 49, 7 × 14

Expected answer: [(1, 98), (2, 49), (7, 14)]

Correct? No

🔗 Problem

Problem: List all the factor pairs of the number 26.

Gemma 2B:

 Reasoning: 26 = 1 x 26, 2 x 13.
The factor pairs of 26 are (1, 26) and (2, 13).
### Answer: (1, 26) and (2, 13)

Expected answer: [(1, 26), (2, 13)]

Correct? Yes

🔗 Problem

Problem: Write down all factor pairs of 59.

Gemma 2B:

 Reasoning: 59 is a prime number. Therefore, the only factor pair of 59 is 1 and 59.
### Answer: 1 and 59

Expected answer: [(1, 59)]

Correct? Yes

🔗 Problem

Problem: Find out all factor pairs of 20.

Gemma 2B:

 Reasoning: 20 = 2*10 = 4*5 = 20*1
### Answer: 2*10, 4*5, 20*1

Expected answer: [(1, 20), (2, 10), (4, 5)]

Correct? Yes

🔗 Problem

Problem: Write down all factor pairs of 20.

Gemma 2B:

 Reasoning: 20 = 1*20 = 2*10 = 4*5
The factor pairs of 20 are (1,20), (2,10), and (4,5).
### Answer: (1,20), (2,10), (4,5)

Expected answer: [(1, 20), (2, 10), (4, 5)]

Correct? No

🔗 Problem

Problem: Please list down all factor pairs of 13.

Gemma 2B:

 Reasoning: 13 is a prime number. It has only two factors, 1 and 13.
### Answer: 1 and 13

Expected answer: [(1, 13)]

Correct? Yes

🔗 Problem

Problem: Find all factor pairs of 81.

Gemma 2B:

 Reasoning: 81 = 9*9 = 3*3*3*3 = 3^4
81 has 5 factor pairs: (1,81), (3,27), (9,9), (27,3), (81,1)
### Answer: (1,81), (3,27), (9,9), (27,3), (81,1)

Expected answer: [(1, 81), (3, 27), (9, 9)]

Correct? No

🔗 Problem

Problem: List all factor pairs of 76.

Gemma 2B:

 Reasoning: 76 = 2 × 2 × 19.
The factor pairs of 76 are (1, 76), (2, 38), (4, 19), and (76, 1).
### Answer: (1, 76), (2, 38), (4, 19), (76, 1)

Expected answer: [(1, 76), (2, 38), (4, 19)]

Correct? Yes

🔗 Problem

Problem: Write down all factor pairs of 50.

Gemma 2B:

 Reasoning: 50 = 1*50, 2*25, 5*10, 10*5, 25*2, 50*1
### Answer: 1*50, 2*25, 5*10, 10*5, 25*2, 50*1

Expected answer: [(1, 50), (2, 25), (5, 10)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of the number 76.

Gemma 2B:

 Reasoning: 76 = 2 x 2 x 19
The factor pairs of 76 are (1, 76), (2, 38), (4, 19), (19, 4), (38, 2), and (76, 1).
### Answer: (1, 76), (2, 38), (4, 19), (19, 4), (38, 2), (76, 1)

Expected answer: [(1, 76), (2, 38), (4, 19)]

Correct? Yes

🔗 Problem

Problem: List all factor pairs of 56.

Gemma 2B:

 Reasoning: 56 = 2 × 2 × 2 × 7
The factor pairs of 56 are (1, 56), (2, 28), (4, 14), (7, 8), and (8, 7).
### Answer: (1, 56), (2, 28), (4, 14), (7, 8), and (8, 7)

Expected answer: [(1, 56), (2, 28), (4, 14), (7, 8)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of the number 44.

Gemma 2B:

 Reasoning: 44 = 2 × 2 × 11
The factor pairs of 44 are (1, 44), (2, 22), (4, 11), and (44, 1).
### Answer: (1, 44), (2, 22), (4, 11), (44, 1)

Expected answer: [(1, 44), (2, 22), (4, 11)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of 5.

Gemma 2B:

 Reasoning: 5 = 1 x 5
### Answer: 1 x 5

Expected answer: [(1, 5)]

Correct? Yes

🔗 Problem

Problem: Identify all factor pairs of the number 95.

Gemma 2B:

 Reasoning: 95 = 5 × 19
95 = 1 × 95
95 = 5 × 19
95 = 1 × 95
### Answer: 1 × 95, 5 × 19

Expected answer: [(1, 95), (5, 19)]

Correct? Yes

🔗 Problem

Problem: Please list all the factor pairs of 36.

Gemma 2B:

 Reasoning: 36 = 1*36 = 2*18 = 3*12 = 4*9 = 6*6
The factor pairs of 36 are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6).
### Answer: (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6)

Expected answer: [(1, 36), (2, 18), (3, 12), (4, 9), (6, 6)]

Correct? Yes

🔗 Problem

Problem: Compute all the factor pairs of the number 59.

Gemma 2B:

 The factor pairs of 59 are: (1,59) and (59,1).

Expected answer: [(1, 59)]

Correct? No

🔗 Problem

Problem: What are all the factor pairs of 3?

Gemma 2B:

 Reasoning: 3 is a prime number, so it has only two factor pairs: 1×3 and 3×1.
### Answer: 1×3 and 3×1

Expected answer: [(1, 3)]

Correct? Yes

🔗 Problem

Problem: Could you list all factor pairs of 51?

Gemma 2B:

 Reasoning: 51 = 1 x 51, 3 x 17
### Answer: 1 x 51, 3 x 17

Expected answer: [(1, 51), (3, 17)]

Correct? Yes

🔗 Problem

Problem: List all factor pairs of 50.

Gemma 2B:

 Reasoning: 50 = 1*50, 2*25, 5*10, 10*5, 25*2, 50*1
### Answer: 1*50, 2*25, 5*10, 10*5, 25*2, 50*1

Expected answer: [(1, 50), (2, 25), (5, 10)]

Correct? Yes

🔗 Problem

Problem: Write down all factor pairs of 47.

Gemma 2B:

 Reasoning: 47 is a prime number. It has only two factors, 1 and 47.
### Answer: 1 and 47

Expected answer: [(1, 47)]

Correct? Yes

🔗 Problem

Problem: Write down all factor pairs of 51.

Gemma 2B:

 Reasoning: 51 = 1 x 51, 3 x 17
### Answer: 1 x 51, 3 x 17

Expected answer: [(1, 51), (3, 17)]

Correct? Yes

🔗 Problem

Problem: List all factor pairs of 60.

Gemma 2B:

 Reasoning: 60 = 1*60 = 2*30 = 3*20 = 4*15 = 5*12 = 6*10 = 10*6 = 12*5 = 15*4 = 20*3 = 30*2 = 60*1
### Answer: (1,60), (2,30), (3,20), (4,15), (5,12), (6,10), (10,6), (12,5), (15,4), (20,3), (30,2), (60,1)

Expected answer: [(1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10)]

Correct? No

🔗 Problem

Problem: List all factor pairs of 43.

Gemma 2B:

 Reasoning: 43 is a prime number, so it has only two factor pairs: 1 and 43, and 43 and 1.
### Answer: 1 and 43, 43 and 1

Expected answer: [(1, 43)]

Correct? Yes

🔗 Problem

Problem: List all factor pairs of 70.

Gemma 2B:

 Reasoning: 70 = 2 × 5 × 7
The factor pairs of 70 are (1, 70), (2, 35), (5, 14), (7, 10), and (10, 7).
### Answer: (1, 70), (2, 35), (5, 14), (7, 10), and (10, 7)

Expected answer: [(1, 70), (2, 35), (5, 14), (7, 10)]

Correct? Yes

🔗 Problem

Problem: Please list all the factors of the number 2.

Gemma 2B:

 Reasoning: 2 is a prime number, so it has only two factors: 1 and 2.
### Answer: 1, 2

Expected answer: [(1, 2)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of 49.

Gemma 2B:

 Reasoning: 49 = 1 x 49 = 7 x 7
### Answer: 1 x 49, 7 x 7

Expected answer: [(1, 49), (7, 7)]

Correct? Yes

🔗 Problem

Problem: Identify all factor pairs of 17.

Gemma 2B:

 Reasoning: 17 is a prime number. Therefore, the only factor pair of 17 is 1 and 17.
### Answer: 1 and 17

Expected answer: [(1, 17)]

Correct? Yes

🔗 Problem

Problem: Find all the factor pairs of 35.

Gemma 2B:

 Reasoning: 35 = 5 × 7, so the factor pairs of 35 are (1, 35), (5, 7), (7, 5), and (35, 1).
### Answer: (1, 35), (5, 7), (7, 5), (35, 1)

Expected answer: [(1, 35), (5, 7)]

Correct? Yes

🔗 Problem

Problem: Identify all factor pairs of the number 91.

Gemma 2B:

 Reasoning: 91 = 7 × 13
91 = 1 × 91
### Answer: 1 × 91, 7 × 13

Expected answer: [(1, 91), (7, 13)]

Correct? Yes

🔗 Problem

Problem: List all factor pairs of the number 97.

Gemma 2B:

 Reasoning: 97 is a prime number. The only factor pair of 97 is 1 and 97.
### Answer: 1 and 97

Expected answer: [(1, 97)]

Correct? Yes

🔗 Problem

Problem: What are all the factor pairs of 16?

Gemma 2B:

 Reasoning: 16 = 1 x 16 = 2 x 8 = 4 x 4
The factor pairs of 16 are (1, 16), (2, 8), and (4, 4).
### Answer: (1, 16), (2, 8), and (4, 4)

Expected answer: [(1, 16), (2, 8), (4, 4)]

Correct? Yes

🔗 Problem

Problem: Find all the factor pairs of the number 21.

Gemma 2B:

 Reasoning: 21 = 3 × 7.
The factor pairs of 21 are (1, 21) and (3, 7).
### Answer: (1, 21) and (3, 7)

Expected answer: [(1, 21), (3, 7)]

Correct? Yes

🔗 Problem

Problem: Could you determine all the factor pairs of 72?

Gemma 2B:

 Reasoning: 72 = 2 × 2 × 2 × 3 × 3
The factor pairs of 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9).
### Answer: (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9)

Expected answer: [(1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9)]

Correct? Yes

🔗 Problem

Problem: Determine all the factor pairs of 38.

Gemma 2B:

 Reasoning: 38 = 2 × 19.
The factor pairs of 38 are (1, 38), (2, 19), and (38, 1).
### Answer: (1, 38), (2, 19), (38, 1)

Expected answer: [(1, 38), (2, 19)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of 94.

Gemma 2B:

 Reasoning: 94 = 2 x 47, so the factor pairs of 94 are (1, 94) and (2, 47).
### Answer: (1, 94) and (2, 47)

Expected answer: [(1, 94), (2, 47)]

Correct? Yes

🔗 Problem

Problem: List all factor pairs of 32.

Gemma 2B:

 Reasoning: 32 = 1 x 32, 2 x 16, 4 x 8, 8 x 4, 16 x 2, 32 x 1.
### Answer: 1 x 32, 2 x 16, 4 x 8, 8 x 4, 16 x 2, 32 x 1

Expected answer: [(1, 32), (2, 16), (4, 8)]

Correct? Yes

🔗 Problem

Problem: Identify all factor pairs of the number 33.

Gemma 2B:

 Reasoning: 33 = 3 × 11
33 = 1 × 33
### Answer: 1 × 33, 3 × 11

Expected answer: [(1, 33), (3, 11)]

Correct? Yes

🔗 Problem

Problem: Write down all the factor pairs of 59.

Gemma 2B:

 Reasoning: 59 is a prime number. It has only two factors, 1 and 59.
The only factor pair of 59 is (1, 59).
### Answer: (1, 59)

Expected answer: [(1, 59)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of the number 54.

Gemma 2B:

 Reasoning: 54 = 2 x 3 x 3 x 3
The factor pairs of 54 are (1, 54), (2, 27), (3, 18), (6, 9), (9, 6), (18, 3), (27, 2), and (54, 1).
### Answer: (1, 54), (2, 27), (3, 18), (6, 9), (9, 6), (18, 3), (27, 2), and (54, 1)

Expected answer: [(1, 54), (2, 27), (3, 18), (6, 9)]

Correct? Yes

🔗 Problem

Problem: Determine all factor pairs of the number 85.

Gemma 2B:

 Reasoning: 85 = 5 × 17
The factor pairs of 85 are (1, 85), (5, 17), and (85, 1).
### Answer: (1, 85), (5, 17), and (85, 1)

Expected answer: [(1, 85), (5, 17)]

Correct? Yes

🔗 Problem

Problem: Identify all the factor pairs of the number 56.

Gemma 2B:

 Reasoning: 56 = 2 × 2 × 2 × 7
The factor pairs of 56 are (1, 56), (2, 28), (4, 14), (7, 8), and (8, 7).
### Answer: (1, 56), (2, 28), (4, 14), (7, 8), and (8, 7)

Expected answer: [(1, 56), (2, 28), (4, 14), (7, 8)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of the number 24.

Gemma 2B:

 Reasoning: 24 = 1 x 24, 2 x 12, 3 x 8, 4 x 6.
### Answer: 1 x 24, 2 x 12, 3 x 8, 4 x 6

Expected answer: [(1, 24), (2, 12), (3, 8), (4, 6)]

Correct? Yes

🔗 Problem

Problem: What are all the factor pairs of the number 84?

Gemma 2B:

 Reasoning: 84 = 2 × 2 × 3 × 7
The factor pairs of 84 are (1, 84), (2, 42), (3, 28), (4, 21), (6, 14), (7, 12), (12, 7), (14, 6), (21, 4), (28, 3), (42, 2), and (84, 1).
### Answer: (1, 84), (2, 42), (3, 28), (4, 21), (6, 14), (7, 12), (12, 7), (14, 6), (21, 4), (28, 3), (42, 2), and (84, 1)

Expected answer: [(1, 84), (2, 42), (3, 28), (4, 21), (6, 14), (7, 12)]

Correct? Yes

🔗 Problem

Problem: Identify all factor pairs of the number 36.

Gemma 2B:

 Reasoning: 36 = 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6.
### Answer: 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6

Expected answer: [(1, 36), (2, 18), (3, 12), (4, 9), (6, 6)]

Correct? Yes

🔗 Problem

Problem: What are all the factor pairs of 85?

Gemma 2B:

 Reasoning: 85 = 5 × 17
The factor pairs of 85 are (1, 85), (5, 17), (17, 5), and (85, 1).
### Answer: (1, 85), (5, 17), (17, 5), (85, 1)

Expected answer: [(1, 85), (5, 17)]

Correct? Yes

🔗 Problem

Problem: Identify all factor pairs of the number 34.

Gemma 2B:

 Reasoning: 34 = 2 x 17
The factor pairs of 34 are (1, 34) and (2, 17).
### Answer: (1, 34) and (2, 17)

Expected answer: [(1, 34), (2, 17)]

Correct? Yes

🔗 Problem

Problem: Determine all factor pairs of 88.

Gemma 2B:

 Reasoning: 88 = 2 × 2 × 2 × 11.
The factor pairs of 88 are (1, 88), (2, 44), (4, 22), (8, 11), (11, 8), (22, 4), (44, 2), and (88, 1).
### Answer: (1, 88), (2, 44), (4, 22), (8, 11), (11, 8), (22, 4), (44, 2), (88, 1)

Expected answer: [(1, 88), (2, 44), (4, 22), (8, 11)]

Correct? Yes

🔗 Problem

Problem: Write down all factor pairs for the number 83.

Gemma 2B:

 Reasoning: 83 is a prime number. It has only two factors: 1 and 83.
### Answer: 1 and 83

Expected answer: [(1, 83)]

Correct? Yes

🔗 Problem

Problem: What are all the factor pairs of 60?

Gemma 2B:

 Reasoning: 60 = 2*2*3*5
The factor pairs of 60 are: (1,60), (2,30), (3,20), (4,15), (5,12), (6,10), (10,6), (12,5), (15,4), (20,3), (30,2), (60,1)
### Answer: (1,60), (2,30), (3,20), (4,15), (5,12), (6,10), (10,6), (12,5), (15,4), (20,3), (30,2), (60,1)

Expected answer: [(1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10)]

Correct? No

🔗 Problem

Problem: Write down all factor pairs of 58.

Gemma 2B:

 Reasoning: 58 = 1 x 58, 2 x 29, 58 x 1, 29 x 2.
### Answer: 1 x 58, 2 x 29, 58 x 1, 29 x 2

Expected answer: [(1, 58), (2, 29)]

Correct? Yes

🔗 Problem

Problem: Please list all of the factor pairs of the number 40.

Gemma 2B:

 Reasoning: 40 = 1*40 = 2*20 = 4*10 = 5*8 = 8*5 = 10*4 = 20*2 = 40*1
### Answer: 1*40, 2*20, 4*10, 5*8, 8*5, 10*4, 20*2, 40*1

Expected answer: [(1, 40), (2, 20), (4, 10), (5, 8)]

Correct? Yes

🔗 Problem

Problem: Identify all the factor pairs of 91.

Gemma 2B:

 Reasoning: 91 = 7 x 13
91 = 1 x 91
### Answer: 1 x 91, 7 x 13

Expected answer: [(1, 91), (7, 13)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of 76.

Gemma 2B:

 Reasoning: 76 = 2 x 38 = 4 x 19 = 1 x 76
The factor pairs of 76 are (2, 38), (4, 19), and (1, 76).
### Answer: (2, 38), (4, 19), and (1, 76)

Expected answer: [(1, 76), (2, 38), (4, 19)]

Correct? Yes

🔗 Problem

Problem: What are all the factor pairs of 13?

Gemma 2B:

 Reasoning: 13 is a prime number, so it has only two factor pairs: 1 and 13, and 13 and 1.
### Answer: 1 and 13, 13 and 1

Expected answer: [(1, 13)]

Correct? Yes

🔗 Problem

Problem: Find all factor pairs of 64.

Gemma 2B:

 Reasoning: 64 = 2*2*2*2*2*2 = 2^6
The factor pairs of 64 are: (1,64), (2,32), (4,16), (8,8)
### Answer: (1,64), (2,32), (4,16), (8,8)

Expected answer: [(1, 64), (2, 32), (4, 16), (8, 8)]

Correct? No

🔗 Problem

Problem: What are all factor pairs of 8?

Gemma 2B:

 Reasoning: 8 = 1 × 8 = 2 × 4
The factor pairs of 8 are (1, 8) and (2, 4).
### Answer: (1, 8) and (2, 4)

Expected answer: [(1, 8), (2, 4)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of 80.

Gemma 2B:

 Reasoning: 80 = 1*80 = 2*40 = 4*20 = 5*16 = 8*10 = 10*8 = 16*5 = 20*4 = 40*2 = 80*1
The factor pairs of 80 are (1,80), (2,40), (4,20), (5,16), (8,10), (10,8), (16,5), (20,4), (40,2), (80,1).
### Answer: (1,80), (2,40), (4,20), (5,16), (8,10), (10,8), (16,5), (20,4), (40,2), (80,1)

Expected answer: [(1, 80), (2, 40), (4, 20), (5, 16), (8, 10)]

Correct? No

🔗 Problem

Problem: Calculate all the factor pairs for the number 96.

Gemma 2B:

 96 = 2 × 2 × 2 × 2 × 2 × 3
96 = 1 × 96
96 = 2 × 48
96 = 3 × 32
96 = 4 × 24
96 = 6 × 16
96 = 8 × 12
96 = 12 × 8
96 = 16 × 6
96 = 24 × 4
96 = 32 × 3
96 = 48 × 2
96 = 96 × 1

Expected answer: [(1, 96), (2, 48), (3, 32), (4, 24), (6, 16), (8, 12)]

Correct? Yes

🔗 Problem

Problem: Calculate all factor pairs of 19.

Gemma 2B:

 Reasoning: 19 is a prime number. Therefore, the only factor pair of 19 is 1 and 19.
### Answer: 1 and 19

Expected answer: [(1, 19)]

Correct? Yes

🔗 Problem

Problem: What are all factor pairs of 37?

Gemma 2B:

 Reasoning: 37 is a prime number, so it has only two factor pairs: 1 and 37, and 37 and 1.
### Answer: 1 and 37, 37 and 1

Expected answer: [(1, 37)]

Correct? Yes

🔗 Problem

Problem: Write down all factor pairs of the number 6.

Gemma 2B:

 Reasoning: 6 = 1 x 6 = 2 x 3
The factor pairs of 6 are (1, 6) and (2, 3).
### Answer: (1, 6) and (2, 3)

Expected answer: [(1, 6), (2, 3)]

Correct? Yes

🔗 Problem

Problem: List down all the factor pairs of 58.

Gemma 2B:

 Reasoning: 58 = 1 x 58, 2 x 29, 58 x 1, 29 x 2
### Answer: 1 x 58, 2 x 29, 58 x 1, 29 x 2

Expected answer: [(1, 58), (2, 29)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of the number 81.

Gemma 2B:

 Reasoning: 81 = 1 x 81 = 3 x 27 = 9 x 9
The factor pairs of 81 are (1, 81), (3, 27), and (9, 9).
### Answer: (1, 81), (3, 27), and (9, 9)

Expected answer: [(1, 81), (3, 27), (9, 9)]

Correct? Yes

🔗 Problem

Problem: Please list all factor pairs of the number 85.

Gemma 2B:

 Reasoning: 85 = 1 x 85, 5 x 17
### Answer: 1 x 85, 5 x 17

Expected answer: [(1, 85), (5, 17)]

Correct? Yes

🔗 Problem

Problem: Write down all factor pairs for the number 93.

Gemma 2B:

 Reasoning: 93 = 1 x 93, 3 x 31, 1 x 93, 3 x 31.
### Answer: 1 x 93, 3 x 31

Expected answer: [(1, 93), (3, 31)]

Correct? Yes

🔗 Problem

Problem: Identify all factor pairs of 24.

Gemma 2B:

 1×24, 2×12, 3×8, 4×6, 6×4, 8×3, 12×2, 24×1

Expected answer: [(1, 24), (2, 12), (3, 8), (4, 6)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of 97.

Gemma 2B:

 Reasoning: 97 is a prime number, so it has only one factor pair, 1 and 97.
### Answer: 1 and 97

Expected answer: [(1, 97)]

Correct? Yes

🔗 Problem

Problem: Identify all factor pairs of the number 57.

Gemma 2B:

 Reasoning: 57 = 3 × 19.
The factor pairs of 57 are (1, 57), (3, 19), (57, 1), and (19, 3).
### Answer: (1, 57), (3, 19), (57, 1), and (19, 3)

Expected answer: [(1, 57), (3, 19)]

Correct? Yes

🔗 Problem

Problem: List down all the factor pairs of 19.

Gemma 2B:

 Reasoning: 19 is a prime number. It has only one factor pair, which is 1 and 19.
### Answer: 1 and 19

Expected answer: [(1, 19)]

Correct? Yes

🔗 Problem

Problem: What are all factor pairs of 38?

Gemma 2B:

 Reasoning: 38 = 2 × 19.
The factor pairs of 38 are (1, 38), (2, 19), and (38, 1).
### Answer: (1, 38), (2, 19), (38, 1)

Expected answer: [(1, 38), (2, 19)]

Correct? Yes

🔗 Problem

Problem: Find all the factor pairs of the number 6.

Gemma 2B:

 Reasoning: 6 = 1 x 6 = 2 x 3
The factor pairs of 6 are (1, 6) and (2, 3).
### Answer: (1, 6) and (2, 3)

Expected answer: [(1, 6), (2, 3)]

Correct? Yes

🔗 Problem

Problem: Write down all factor pairs of 17.

Gemma 2B:

 Reasoning: 17 is a prime number. It has only two factors: 1 and 17.
### Answer: 1 and 17

Expected answer: [(1, 17)]

Correct? Yes

🔗 Problem

Problem: List all factor pairs of 45.

Gemma 2B:

 Reasoning: 45 = 1 x 45, 3 x 15, 5 x 9, 9 x 5, 15 x 3, 45 x 1.
### Answer: 1 x 45, 3 x 15, 5 x 9, 9 x 5, 15 x 3, 45 x 1

Expected answer: [(1, 45), (3, 15), (5, 9)]

Correct? Yes

🔗 Problem

Problem: Write down all factor pairs of 36.

Gemma 2B:

 Reasoning: 36 = 1*36 = 2*18 = 3*12 = 4*9 = 6*6
### Answer: 1*36, 2*18, 3*12, 4*9, 6*6

Expected answer: [(1, 36), (2, 18), (3, 12), (4, 9), (6, 6)]

Correct? Yes

🔗 Problem

Problem: What are all factor pairs of 89?

Gemma 2B:

 Reasoning: 89 is a prime number, so it has only two factor pairs: 1 and 89, and 89 and 1.
### Answer: 1 and 89, 89 and 1

Expected answer: [(1, 89)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of 89.

Gemma 2B:

 Reasoning: 89 is a prime number. It has only one factor pair, 1 and 89.
### Answer: 1 and 89

Expected answer: [(1, 89)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of the number 44.

Gemma 2B:

 Reasoning: 44 = 2 × 2 × 11
The factor pairs of 44 are (1, 44), (2, 22), (4, 11), and (44, 1).
### Answer: (1, 44), (2, 22), (4, 11), (44, 1)

Expected answer: [(1, 44), (2, 22), (4, 11)]

Correct? Yes

🔗 Problem

Problem: Identify all factor pairs of the number 36.

Gemma 2B:

 Reasoning: 36 = 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6.
### Answer: 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6

Expected answer: [(1, 36), (2, 18), (3, 12), (4, 9), (6, 6)]

Correct? Yes

🔗 Problem

Problem: List all possible factor pairs of the number 35.

Gemma 2B:

 Reasoning: 35 = 1 x 35 = 5 x 7
### Answer: 1 x 35, 5 x 7

Expected answer: [(1, 35), (5, 7)]

Correct? Yes

🔗 Problem

Problem: Write down all factor pairs of 22.

Gemma 2B:

 Reasoning: 22 = 1*22 = 2*11
### Answer: 1*22, 2*11

Expected answer: [(1, 22), (2, 11)]

Correct? Yes

🔗 Problem

Problem: Find all the factor pairs of 40.

Gemma 2B:

 Reasoning: 40 = 2 × 2 × 2 × 5
The factor pairs of 40 are (1, 40), (2, 20), (4, 10), (5, 8), (8, 5), (10, 4), (20, 2), and (40, 1).
### Answer: (1, 40), (2, 20), (4, 10), (5, 8), (8, 5), (10, 4), (20, 2), (40, 1)

Expected answer: [(1, 40), (2, 20), (4, 10), (5, 8)]

Correct? Yes

🔗 Problem

Problem: List all the factor pairs of the number 64.

Gemma 2B:

 Reasoning: 64 = 1 x 64, 2 x 32, 4 x 16, 8 x 8.
### Answer: 1 x 64, 2 x 32, 4 x 16, 8 x 8

Expected answer: [(1, 64), (2, 32), (4, 16), (8, 8)]

Correct? Yes

🔗 Problem

Problem: Determine all factor pairs of 30.

Gemma 2B:

 Reasoning: 30 = 2 × 3 × 5.
The factor pairs of 30 are (1, 30), (2, 15), (3, 10), (5, 6).
### Answer: (1, 30), (2, 15), (3, 10), (5, 6)

Expected answer: [(1, 30), (2, 15), (3, 10), (5, 6)]

Correct? Yes

🔗 Problem

Problem: List all factor pairs of 59.

Gemma 2B:

 Reasoning: 59 is a prime number. Therefore, the only factor pair of 59 is 1 and 59.
### Answer: 1 and 59

Expected answer: [(1, 59)]

Correct? Yes

🔗 Problem

Problem: List all factor pairs of 18.

Gemma 2B:

 Reasoning: 18 = 1 x 18, 2 x 9, 3 x 6.
### Answer: 1 x 18, 2 x 9, 3 x 6

Expected answer: [(1, 18), (2, 9), (3, 6)]

Correct? Yes

🔗 Problem

Problem: Please list all the factor pairs of 61.

Gemma 2B:

 Reasoning: 61 is a prime number, so it has only one factor pair, 1 and 61.
### Answer: 1 and 61

Expected answer: [(1, 61)]

Correct? Yes

🔗 Problem

Problem: What are all of the factor pairs of 86?

Gemma 2B:

 Reasoning: 86 = 2 × 43 = 1 × 86
The factor pairs of 86 are (2, 43) and (1, 86).
### Answer: (2, 43) and (1, 86)

Expected answer: [(1, 86), (2, 43)]

Correct? Yes

🔗 Problem

Problem: List out all factor pairs of 57.

Gemma 2B:

 Reasoning: 57 = 1 x 57, 3 x 19
### Answer: 1 x 57, 3 x 19

Expected answer: [(1, 57), (3, 19)]

Correct? Yes

🔗 Problem

Problem: What are all factor pairs of 38?

Gemma 2B:

 Reasoning: 38 = 2 × 19, so the factor pairs of 38 are (1, 38) and (2, 19).
### Answer: (1, 38) and (2, 19)

Expected answer: [(1, 38), (2, 19)]

Correct? Yes

🔗 Problem

Problem: Please list all factor pairs of 27.

Gemma 2B:

 Reasoning: 27 = 3*9 = 1*27
The factor pairs of 27 are (1,27) and (3,9).

Expected answer: [(1, 27), (3, 9)]

Correct? No

🔗 Problem

Problem: List all the factor pairs of the number 78.

Gemma 2B:

 Reasoning: 78 = 2 x 3 x 13.
The factor pairs of 78 are (1, 78), (2, 39), (3, 26), (6, 13), (13, 6), (26, 3), (39, 2), and (78, 1).
### Answer: (1, 78), (2, 39), (3, 26), (6, 13), (13, 6), (26, 3), (39, 2), (78, 1)

Expected answer: [(1, 78), (2, 39), (3, 26), (6, 13)]

Correct? Yes

🔗 Problem

Problem: List out all the factor pairs of 23.

Gemma 2B:

 Reasoning: 23 is a prime number, so it has only one factor pair.
23 = 1 x 23
### Answer: 1 x 23

Expected answer: [(1, 23)]

Correct? Yes

🔗 Problem

Problem: List down all the factor pairs of 2.

Gemma 2B:

 2 = 1 x 2
### Answer: 1 x 2

Expected answer: [(1, 2)]

Correct? Yes

🔗 Problem

Problem: Write down all the factor pairs of 49.

Gemma 2B:

 Reasoning: 49 = 1 x 49 = 7 x 7
### Answer: 1 x 49, 7 x 7

Expected answer: [(1, 49), (7, 7)]

Correct? Yes

🔗 Problem

Problem: Identify all the distinct pairs of factors that can multiply to give the number 93.

Gemma 2B:

 Reasoning: 93 = 3 × 31
93 = 1 × 93
93 = 93 × 1
### Answer: 3 × 31, 1 × 93, 93 × 1

Expected answer: [(1, 93), (3, 31)]

Correct? Yes