A Perfect Cube

Number Theory Level 2

What is the smallest natural number which leaves a perfect cube when we divide 108 by that number?

2 solutions

Alex G
Aug 14, 2016

$108 = 2^2 \cdot 3^3$

Therefore the only numbers which satisfy the condition are $2^2=4$ and 108, which leave $3^3=27$ and $1^3 = 1$ , respectively.

$\boxed{4}$

Pratyush Atolia
Jan 12, 2018

We can factories the number- 108 =2×2×(3×3×3)