Question

find the smallest number by which 657 must be multipled to obtain a perfect cube​

Answer 1

Answer:

Explanation:

Prime factorising 675, we get,

675=5×5×3×3×3 =3  

3

×5  

2

.

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

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

So we need to multiply another 5 in the factorization to make 675 a perfect cube.

Hence, the smallest number by which 675 must be multiplied to obtain a perfect cube is 5