Question

find the smallest number by which 6048 should be multiplied and divided so that the product and the quotient obtained is a perfect cube

Answer 1

Answer:

Prime factorising 36, we get,

36=2×2×3×3=2

2

×3

2

.

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 2's is 2 and number of 3's is 2.

So we need to multiply another 2 and 3 in the factorization to make 36 a perfect cube.

Hence, the smallest number by which 36 must be multiplied to obtain a perfect cube is 2×3=6.

Step-by-step explanation:

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