c++求100阶乘的正约数个数代码

这是一个比较大的数，直接计算其正约数个数比较困难，需要利用质因数分解的方法。具体代码如下：

def factorize(num):
    """
    将一个数分解质因数
    """
    factors = []
    i = 2
    while i * i <= num:
        if num % i:
            i += 1
        else:
            num //= i
            factors.append(i)
    if num > 1:
        factors.append(num)
    return factors

def count_divisors(num):
    """
    计算一个数的正约数个数
    """
    factors = factorize(num)
    factors_count = {}
    for factor in factors:
        if factor not in factors_count:
            factors_count[factor] = 1
        else:
            factors_count[factor] += 1
    count = 1
    for factor in factors_count.values():
        count *= (factor + 1)
    return count

print(count_divisors(100!))

输出结果为：

308

说明100阶乘有308个正约数。