is 1188 a perfect cube?if not by which smallest natural number should 1100 be divided so that the quotient is a perfect cube

**Given** number = 1188

It can be prime factorized as:

1188 = 2 × 2 × 3 × 3 × 3 × 11 ... (1)

Here, only 3 appears in the form of triplet and we know that in order to have a number as a perfect cube it must have all the numbers in triplet.

So, if we multiply (1) by 2 and 11 × 11 then we will get

2 × 2 × 3 × 3 × 3 × 11 × 2 × 11 × 11 = 2 × 2 × 2 × 3 × 3 × 3 × 11 × 11 × 11 = 287496

Now, all the number's i.e., 2, 3 and 11 appears in triplet.

So, 287496 will be the perfect cube of 2 × 3 × 11 = 66.

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