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**jstarks44444** Let m,n be elements of the Natural numbers. **Prove that if m divides n and p is a prime factor of n that is not a prime factor of m, then m divides n/p**

The following facts can be used:

*Every integer >= 2 can be factored into primes.

*Let m,n be in the Integers:

- gcd(m, n) divides both m and n

- unless m and n are both 0, gcd(m, n) > 0

- every integer that divides both m and n also divides gcd(m, n)

*For all k,m,n that are elements of the Integers,

-gcd(km, kn) = |k|gcd(m, n)

*Let p be prime and m,n be elements of the Natural numbers. If p|mn then p|m or p|n

(Euclid's Lemma)

*Every integer >= 2 can be factored uniquely into primes.

Some insight into this problem would be really beneficial, thanks a lot!