------
## 最终结论
```python
from collections import defaultdict
import math

class UnionFind:
    def __init__(self, size):
        self.parent = list(range(size))
        self.rank = [1] * size

    def find(self, p):
        if self.parent[p] != p:
            self.parent[p] = self.find(self.parent[p])
        return self.parent[p]

    def union(self, p, q):
        rootP = self.find(p)
        rootQ = self.find(q)
        
        if rootP != rootQ:
            if self.rank[rootP] > self.rank[rootQ]:
                self.parent[rootQ] = rootP
            elif self.rank[rootP] < self.rank[rootQ]:
                self.parent[rootP] = rootQ
            else:
                self.parent[rootQ] = rootP
                self.rank[rootP] += 1

def largestComponentSize(A):
    n = len(A)
    uf = UnionFind(n)
    
    # Mapping from prime factors to the index of the numbers in A
    prime_to_index = defaultdict(list)
    
    for index, number in enumerate(A):
        # Find all factors greater than 1
        for factor in range(2, int(math.sqrt(number)) + 1):
            if number % factor == 0:
                prime_to_index[factor].append(index)
                while number % factor == 0:
                    number //= factor
        if number > 1:  # If there's any prime factor left greater than sqrt(number)
            prime_to_index[number].append(index)

    # Union indices that share common factors
    for indices in prime_to_index.values():
        for i in range(1, len(indices)):
            uf.union(indices[0], indices[i])

    # Calculate the size of each component
    component_size = defaultdict(int)
    for i in range(n):
        root = uf.find(i)
        component_size[root] += 1

    return max(component_size.values())
```