inRange()这个函数如何实现，反迭代为何就能判断阶乘计算结果是否超最大值

夜的奏鸣曲

#include <iostream>
#include <climits>

class Factorial
{
public:
    Factorial(unsigned short num);
    unsigned long getFactorial();
    bool inRange();

private:
    unsigned short num;
};

Factorial::Factorial(unsigned short num)
{
    this->num = num;
}

unsigned long Factorial::getFactorial()
{
    unsigned long sum = 1;

    for( int i=1; i <= num; i++ )
    {
        sum *= i;
    }

    return sum;
}

bool Factorial::inRange()
{
    unsigned long max = ULONG_MAX;

    for( int i=num; i >= 1; --i )
    {
        max /= i;
    }

    if( max < 1 )
        return false;
    else
        return true;
}

int main()
{
    unsigned short num = 0;

    std::cout << "请输入一个整数: ";
    std::cin >> num;

    Factorial fac(num);

    if( fac.inRange() )
    {
        std::cout << num << "的阶乘值是" << fac.getFactorial() << "\n\n";
    }
    else
    {
        std::cout << "您所输入的值太大!\n\n";
    }

    return 0;
}

Croper

简单的移项啊
max=ulong_max/1/2/3/4/.../num=ulong_max/(1*2*3*..*num)=ulong_max/(num!);
max<1   ==>   ulong_max<num!;
所以溢出