Question

Find the smallest number by which 2560 must be multiplied so that the product is

a perfect cube.​

Answer 1

Answer:

25

Step-by-step explanation:

2560=2⁹×5

if we multiply it by 5² then the number would be 2⁹×5³=(2³×5)³ it is a perfect cube number

Answer 2

Prime factorising 2560, we get,

2560=2

9

×5.

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

Here, number of 2's is 9 and number of 5's is 1.

So we need to multiply another 5

2

in the factorization to make 2560 a perfect cube.

Hence, the smallest number by which 2560 must be multiplied to obtain a perfect cube is 5

2

=25.