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Q.

Find the smallest number by which the 81 number must be divided to obtain a perfect cube.


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a

1

b

2

c

4

d

3 

answer is D.

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Detailed Solution

Prime factorization 81,
we get,
81=3×3×3×3=3Question ImageWe know,
A perfect cube has multiples of 3 as powers of prime factors.
Here,
Number of 3's is 4.
So we need to divide the factorization by 3 to make 81 a perfect cube.
Hence, the smallest number by which 81 must be divided to obtain a perfect cube is 3.
 
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