Question

Suppose $b$ is a positive integer such that $\frac{2^4}{b^2}$ is also an integer. What are the possible values of $b$?

Answer 1

Given b will be a positive integer

$\frac{2^4}{b^2}$ will be integer so the possible values of b will be

when b=1

$\frac{2^4}{1^2}=\frac{16}{1}=16$

when b=2

$\frac{2^4}{2^2}=\frac{16}{4}=4$

when b=3

$\frac{2^4}{3^2}=\frac{16}{9}=1.77$

when b=4

$\frac{2^4}{4^2}=\frac{16}{16}=1$

possible values of b will be 1,2,4

as when b is 3 $\frac{2^4}{b^2}$ is not an integer and when b exceeds 4 again it will not be an integer.