The number of divisors(约数) about Humble Numbers

• A number whose only prime factors are 2,3,5 or 7 is called a humble number. The sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, ... shows the first 20 humble numbers.
• Now given a humble number, please write a program to calculate the number of divisors about this humble number.For examle, 4 is a humble,and it have 3 divisors(1,2,4);12 have 6 divisors.
• Input
• The input consists of multiple test cases. Each test case consists of one humble number n,and n is in the range of 64-bits signed integer. Input is terminated by a value of zero for n.
• Output
  For each test case, output its divisor number, one line per case.
• Sample Input
• 4
• 12
• 0
• Sample Output
• 3
• 6

  • 正解用到了算数基本定理
    如果会了这个，问题就迎刃而解

    点击查看代码

    	long long n;
    	while(scanf("%lld",&n)&&n)
    	{
    		long long a,b,c,d;
    		for(a=0;n%2==0;n/=2)
    			a++;
    		for(b=0;n%3==0;n/=3)
    			b++;
    		for(c=0;n%5==0;n/=5)
    			c++;
    		for(d=0;n%7==0;n/=7)
    			d++;
    		printf("%lld\n",(1+a)*(1+b)*(1+c)*(1+d));
    	}