Suppose nm N and nm Prove that n gcdm nSolutionGiven nm the

Suppose n,m N and n|m. Prove that n = gcd(m, n).

Solution

Given n|m then m= kn for k=1,2,3,4...........

gcd(m,n)=gcd (kn,n)

commom divisors are factors of n

greatest of them is n

so gcd(m,n)=n