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Q.


What will be the smallest number by which 192 must be divided to obtain a perfect cube?

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a

2

b

3

c

4

d

5 

answer is B.

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Detailed Solution

We need to find the smallest number by which 192 must be divided to obtain a perfect cube.
Factoring 192 with the smallest divisor:
192=2×2×2×2×2×2×3  
The number is not a perfect cube as 3 does not occur in triplets.
So, we will divide by 3 on both sides to make a triplet:
192 3 = 2×2×2×2×2×2×3 3 =2×2×2×2×2×2  
Now, it is a perfect cube.
Hence, we divide 192 by 3 to make it a perfect cube.
Therefore, option 2 is correct.
 
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