Question

what is the smallest number by which 3922 may be divided so that the product is a perfect cube​

Answer 1

Answer:

Prime factorising 392, we get,

392=2×2×2×7×7

=2

3

×7

2

.

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

Here, number of 2's is 3 and number of 7's is 2.

So we need to multiply another 7 to the factorization to make 392 a perfect cube.

Hence, the smallest number by which 392 must be multiplied to obtain a perfect cube is 7.