Question

Find the smallest number by which the following numbers should be multiplied to obtain a perfect cube. (a) 3087 (b) 2560

Answer 1

Check each number's prime factorization, then add any factors necessary to make each one a cube.

(a) 3

`3087 = 3^2 * 7^3 \implies \boxed{3}*3087 = (3*7)^3 \implies 9261=21^3`

(b) 25

`2560 = 2^9*5^1 \implies \boxed{5^2}*2560 = \left(2^3*5\right)^3 \implies 64000 = 40^3`