Question

Find the smallest number by 10976 must be divided so that the quotient is a perfect cube?
Please Give Step By Step Explanation.​

Answer 1

Prime factorising 10976, we get,

10976=2×2×2×2×2×7×7×7

⠀⠀⠀⠀=2⁵$&times$7³

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

Here, number of 2's is 5 and number of 7's is 3.

So we need to multiply another 2 to the factorization to make 10976 a perfect cube.

Hence, the smallest number by which 10976 must be multiplied to obtain a perfect cube is 2.

Answer 2

Answer:

Prime factorising 10976, we get,

10976=2×2×2×2×2×7×7×7

=2

5

×7

3

.

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

Here, number of 2's is 5 and number of 7's is 3.

So we need to multiply another 2 to the factorization to make 10976 a perfect cube.

Hence, the smallest number by which 10976 must be multiplied to obtain a perfect cube is 2