Question

Find the smallest number by which 27783 must be multiplied to get a perfect cube

• A. 3
• B. 9
• C. 21
• D. 49

Answer 1

The correct option is B

9

The prime factor of 27783 are

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

For a perfect cube, the prime factor should form a triplet.

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

Clearly, 27783 must be multiplied by $3\times 3$ , to make it a perfect cube.

So, 27783 should be multiplied by 9.