How to check 25! is divisible by 9317? asked 27 Nov '16, 23:24

9317= 7x11x11x11 so 25! should contain 3 11's in it's prime factorization but it contains only 2 (ie 11,22(=11*2)) so not divisible. answered 27 Nov '16, 23:35

The algorithm is that first prime factorize the divisor(find the powers of all prime factors of the divisor in this case 9317 = 7^1*11^3).This is easy. Next check if the dividend has all these prime factors. In this case of 25! you can easily find multiples of 11 and check how many are there multiples of 7 and so on. If the dividend at least has all the prime factors of the divisor then it is divisible else it is not. answered 29 Nov '16, 21:32
