Thread: Greatest Common Divisor Proof

Some help with the following proof would be appreciated:

Prove that for all k,m,n in the set of Integers,

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


We have the following propositions already at our disposal.
*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)

Originally Posted by jstarks44444

Some help with the following proof would be appreciated:

Prove that for all k,m,n in the set of Integers,

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


We have the following propositions already at our disposal.
*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)