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Q.

If 9720 is a perfect cube, then the smallest number by which it should be divided to get a perfect cube is:


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a

30

b

35

c

40

d

45 

answer is D.

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Detailed Solution

The given number is 9720  .
The prime factors of 9720   are,
9720=2×2×2×3×3×3×3×3×5  
Here 2   is grouping in one triplet, 3   is grouping in one triplet.
But a pair of 3   and single 5   does not occur in triplets.
So, 9720   is not a perfect cube.
To make 9720   a perfect cube, there should be triplets of prime factors.
There is one triplet of 2   and one triplet of 3  .
Another pair of 3   and 5   is single.
So, the least number by which 9720   be divided to make it a perfect cube is,
3×3×5=45   9720=2×2×2×3×3×3×3×3×5   9720 45 = 2×2×2×3×3×3×3×3×5 3×3×5  
216=2×2×2×3×3×3  
which is a cube number.
The least number that divides 9720 to get the cube number is 45  .
Hence, option 4 is correct.
 
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