Is 2880 a perfect cube? If not, by which smallest natural number should 2880 be divided so that the quotient is a perfect cube?

Hint – In order to solve this problem first take the LCM of 2880 and then multiply the numbers which are not in pairs of three and then divide 2880 with the number obtained. Doing this will solve your problem and you will get the right answer.

Complete step-by-step answer:

$ \Rightarrow $2880=3×3×4×4×4×5

The primes 3 and 5 do not appear in groups of three. So, 2880 is not a perfect cube.

In the factorization of 2880 the prime 3 appears only two times and the prime 5 appears once.

So, if we divide 2880 by 3×5×5=75, then the prime factorisation of the quotient will not contain 3 and 5.

Hence, the smallest natural number by which 2880 should be divided to make it a perfect cube is 75.

Hence, the answer is 75.

Note – In this problem you need to take the LCM of 2880 then you have to find the numbers which do not make a pair of three and divide 2880 by that number only. Be careful between cube and square root since sometimes we use the concept of square root instead of cube roots. Proceeding like this will solve this problem.