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

400 ×
**
1/2
**
×
**
1/
**
**
5
**
×
**
1/5
**
= 2 × 2 × 2 × 2 × 5 × 5 ×
**
1/2
**
×
**
1/5
**
×
**
1/5
**

= 2 × 2 × 2

Now, it becomes a perfect cube.

So, we divide 400 by 2 × 5 × 5

i.e.
**
50
**
to make it a perfect cube

So, our number becomes

400 ×
**
1/2
**
×
**
1/
**
**
5
**
×
**
1/5
**
= 2 × 2 × 2 × 2 × 5 × 5 ×
**
1/2
**
×
**
1/5
**
×
**
1/5
**

= 2 × 2 × 2

Now, it becomes a perfect cube.

So, we divide 400 by 2 × 5 × 5

i.e.
**
50
**
to make it a perfect cube