Why does this factorization program fail for numbers greated than 102030405060708001?

Question

Following is a factorization program in Python. It works fine till 102030405060708001 but produces incorrect results for greater integers. Why is this so?

import math

a = []


def prime(n):
    isPrime = True
    for r in range(2,int(n**(1/2)+1)):
        if n%r == 0:
            isPrime = False
    return isPrime


def factor(number):
    if prime(number):
        a.append(int(number))

    for r in range(2, 1 + int(number**(1/2))):
        if number%r == 0:
            a.append(r)
            number = number/r
            factor(number)
            break
    
    return a        


number = int(input("Enter a number whose factors you want:"))
factor(number)
print(f"Factor of {number} are ", end = ": ")
print(*a, sep = ' X ')    
print(math.prod(a))

Example Factor of 102030405060708001 are : 1867601 X 54631800401. And the product of these factors is 102030405060708001

Factor of 102030405060708002 are : 2 X 2 X 2 X 2 X 2 X 3 X 3 X 5 X 5 X 5 X 6133 X 462119341. But the product of these factors is 102030405060708000

Factor of 102030405060708003 are : 3 X 2 X 2 X 2 X 2 X 2 X 3 X 5 X 5 X 5 X 6133 X 462119341. But the product of these factors is 102030405060708000