Question

Find the smallest positive number by which 2560 must be multiplied so that the product is a perfect cube.

• A. 50
• B. 25
• C. 60
• D. 10

Answer 1

The correct option is B 25

Factorising 2560 into prime factors.

$\begin{array}{cc}2& 2560\\ 2& 1280\\ 2& 640\\ 2& 320\\ 2& 160\\ 2& 80\\ 2& 40\\ 2& 20\\ 2& 10\\ 5& 5\\ & 1\end{array}$

$2560=\underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}\times 5$
Making them in groups of 3 equal factors, we are left with 5
$\therefore$ To make it into a group of 3, we have to multiply it by $5\times 5$ i.e. by 25.
Hence, the smallest number by which it must be multiplied to make it a perfect cube is 25.