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Q.


What will be the smallest number by which 135 must be divided to obtain a perfect cube?

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a

3

b

2

c

4

d

5 

answer is D.

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Detailed Solution

We need to find the smallest number by which 135 must be divided to obtain a perfect cube.
Factoring 135 with the smallest divisor:
135=3×3×3×5  
The number is not a perfect cube as 5 does not occur in triplets.
So, we will divide by 5 on both sides to make a triplet:
135 5 = 3×3×3×5 5 =3×3×3  
Now, it is a perfect cube.
Hence, we divide 135 by 5 to make it a perfect cube.
Therefore, option 4 is correct.
 
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What will be the smallest number by which 135 must be divided to obtain a perfect cube?