Suppose a and b are natural numbers Show that if gcdab1 then

Suppose a and b are natural numbers. Show that if gcd(a,b)>1, then b divides a or b is not prime.

Solution

Case 1: b is prime

Then , gcd(a,b)=1 or b

But gcd(a,b)>1

So, gcd(a,b)=b

Hence, a is a multiple of b

ie b divides a

Case 2 : b is not prime.

There is nothing to prove.