A P-smooth number or P-friable number is an integer whose largest prime factor is less than or equal to P. Given N and P, we need to write a program to check whether it is P-friable or not.
Input : N = 24 , P = 7 Output : YES Explanation : The prime divisors of 24 are 2 and 3 only. Hence its largest prime factor is 3 which is less than or equal to 7, it is P-friable. Input : N = 22 , P = 5 Output : NO Explanation : The prime divisors are 11 and 2, hence 11>5, so it is not a P-friable number.
The approach will be to prime factorize the number and store the maximum of all the prime factors. We first divide the number by 2 if it is divisible, then we iterate from 3 to Sqrt(n) to get the number of times a prime number divides a particular number which reduces every time by n/i and store the prime factor i if its divides N. We divide our number n (by prime factors) by its corresponding smallest prime factor till n becomes 1. And if at the end n > 2, it means its a prime number, so we store that as a prime factor as well. At the end the largest factor is compared with p to check if it is p-smooth number or not.
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Improved By : jit_t