Question

The sum of the digits of the smallest number by
which 6144 is to be divided, so that the quotient
becomes a perfect cube is
(1) 6 (2) 3
(3) 7 (4) 5

Answer 1

Let us do prime factorisation of 6144

6144 = 2x2x2x2x2x2x2x2x2x2x2x3

Let us group them in 3s

2x2x2 2x2x2 2x2x2 2x 2x 3

If we divide 6144 by 2x2x3 then we will get the perfect cube of 8

so the smallest nuber that we can divide 6144 so that we get perfect cube is 12

sum of digits of 12 = 1+2

= 3 is answer

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