1
Question
Is 53240 a perfect cube ? If not, then by which smallest natural number should 53240 be divided so that the quotient is a perfect cube?
Is 53240 a perfect cube ? If not, then by which smallest natural number should 53240 be divided so that the quotient is a perfect cube?
Open in App
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 divide 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.
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 divide 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.
Suggest Corrections
31
Similar questions
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
