Question

Which is the smallest number that must be multiplied to 77175 to make it a perfect cube?

• A. 35
• B. 15
• C. 30
• D. 21

Answer 1

The correct option is B

15

The prime factor of 77175 are

$=3\times 3\times 5\times 5\times 7\times 7\times 7=(7\times 7\times 7\times )\times 3\times 3\times 5\times 5$

For perfect cube, prime factor should form triplet.

Here, we can see, 7's are forming a triplet, but 5's and 3's are not.

Clearly, 77175 must be multiplied by $5\times 3$, to make it a perfect cube.

So, 77175 should be multiplied by 15.