Question

List all the positive integer divisors of 3^s5^t, where s,t are integers and s,t >0. If r,s,t are positive integers, how many positive divisors does 2^r3^s5^t have? Please explain the answer, I am not sure how to get the result.

Answer 1

3^s has s divisors .i.e.,3^1,3^2,3^3,.....,3^s or have s divisors
similarly 5^t has t divisors.
hence 3^s5^t has s+t+s*t divisors