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

$3087 = 3^2 \times 7^3 \implies \boxed{3}\times3087 = (3\times7)^3 \implies 9261=21^3$

(b) 25

$2560 = 2^9\times5^1 \implies \boxed{5^2}\times2560 = \left(2^3\times5\right)^3 \implies 64000 = 40^3$