Question

The smallest natural number by which 1296 be divided to get a perfect cube is

Answer 1

Given,

The main number = 1296

To find,

The smallest natural number that can divide the main number into a perfect cube.

Solution,

First of all we need to perform the prime factorization of the main number. Then we can write the prime factorization in the form of (a³×b³×c³.....so on). The multiplication or the factors which cannot be included into the cube form will be necessary smallest number.

Prime factorization :

1296 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3

1296 = 2³×3³×2×3

The remaining factors are = 2 and 3

The necessary smallest number = 2×3 = 6

Verification :

Division = 1296/6 = 216

Now, 216 is the perfect cube of 3.

Hence, the smallest natural number will be 6.

Answer 2

Answer of this question is 6