Smallest number divided to get a perfect cube

Let’s do this by examples

Finds the smallest number divided to 1125 to get a perfect cube

We see that,

Since 3 does not occur triplets,

we divide by 3 × 3 to make a triplet

So, our number becomes

1125 × 1/ 3 × 1/3   = 3 × 3 × 5 × 5 × 5 × 1/3 × 1/3

     = 5 × 5 × 5

Now, it becomes a perfect cube.

So, we divide 1125 by 3 × 3

i.e. 9 to make it a perfect cube

Finds the smallest number divided to 5324 to get a perfect cube.

We see that,

  5324 = 2 × 2 × 11 × 11 × 11

Here,

2 does not occur in triplets

So, we divide by 2 × 2 to make triplet

So, our number becomes

  5324  × 1/2  × 1/2 = 2 × 2 × 11 × 11 × 11 × 1/2   × 1/2

       = 11 × 11 × 11

Now, it becomes a perfect cube.

So, we divide 5324 by 2 × 2

i.e. 4  to make it a perfect cube

Finds the smallest number divided to 968 to get a perfect cube.

We see that,

  968 = 2 × 2 × 2 × 11 × 11

Here,

11 does not occur in triplets

So, we divide by 11 × 11 to make triplet

So, our number becomes

  968 × 1/11 × 1/ 11 = 2 × 2 × 2 × 11 × 11 × 1/11  × 1/11

          = 2 × 2 × 2

Now, it becomes a perfect cube.