Is 111 prime

Is 111 prime

111 is not prime, 111 = 3 × 37

The product of two primes is 111. What are the two primes

3 and 37

Is n a multiple of prime P and n a multiple of P?
N is the multiple of prime P, n is the multiple of P, and N is an integer
My understanding is n * n = PK, because P is a prime number, so if you want to square an integer, K must be a multiple of N. I can understand it, but how to describe and prove it?
Obviously, I also know that I can't prove whether there is any scientific language in the question?

Proof: if we decompose NPK into the product of prime numbers, then the result is obvious. Proof, I don't know. Here is my own blind proof. Because n = Πni, Ni is prime number, factor of N, I is subscript Π Ni * Πni = KP; because P is prime number, so there exists Ni = P, (why? I don't know.) so there exists n = Πn