Question

find the smallest number by which 10296 must be divided to obtain a perfect cube​

Answer 1

Answer:

the smallest number by which 28672 must be divided to obtain a perfect cube is 7

Answer 2

Prime factorising 10976, we get,

10976=2×2×2×2×2×7×7×7

⠀⠀⠀⠀=2⁵7³

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.