Question

Is 53240 is a perfect cube? If not, then by which smallest natural number should 53240 be divided so that the quotient is a perfect cube?

Answer 1

Solution: 53240 = 2×2×2×11×11×11×5

The prime factor 5 does not appear in a group of three. So, 53240 is not a perfect cube. In the factorisation 5 appears only one time. If we divided the number by 5, then the prime factorisation of the quotient will not contain 5.

So,

53240÷5 = 2×2×2×11×11×11

Hence the smallest number by which 53240 should be divided to make it a perfect cube is 5.

The perfect cube in that case is=10648.

Answer 2

No 53240 is a perfect cube . 5 is the smallest natural number 53240 should be divided so that the quotient is a perfect cube

Given :

The number 53240

To find :

• Check whether 53240 is a perfect cube
• If not the find smallest natural number 53240 should be divided so that the quotient is a perfect cube

Solution :

Step 1 of 3 :

Firstly express the given number as a product of prime factor by using prime factorisation

Here the given number is 53240

53240 = 2 × 2 × 2 × 5 × 11 × 11 × 11

Step 2 of 3 :

Group the factors in triple form . If no factor is left over in grouping (triples) then the number is perfect cube otherwise not

In the prime factorisation of 53240

Number of 2's = 3

Number of 5's = 1

Number of 11's = 3

The number 5 is left over in grouping (triples)

So 53240 is not a perfect cube

Step 3 of 3 :

Find the smallest natural number 53240 should be divided so that the quotient is a perfect cube

Since number of 5's = 1

53240 ÷ 5 = 10648

So 53240 must be divided by 5 so that the quotient 10648 is a perfect cube

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