Question

Is 1296 a perfect cube or not? If not, find the smallest number by which 1296 must be divided so that the quotient is a perfect cube ​

Answer 1

Answer:

Prime factorising 1296, we get,

1296=2×2×2×2×3×3×3×3

         =2  

4

×3  

4

.

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

Here, number of 2's is 4 and number of 3's is 4.

So we need to divide 2 and 3 from the factorization to make 1296 a perfect cube.

Hence, the smallest number by which 1296 must be divided to obtain a perfect cube is 2×3=6

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