Question

Find the smallest number by which 1323 must be multiplied so that the product is a perfect cube

Answer 1

we should multiply 1323 by 7 to become it a perfect cube. because when we factorise it then it did not become it a perfect cube so we have to multiply by 7 and when we multiply it by 7 it become a perfect cube of 21

Answer 2

Answer :-

The smallest number is 7.  

Solution :-

To find the ‘smallest number’ by which 1323 will be multiplied, we need to factorize 1323 as under:

1323 = 3 × 441

1323 = 3 × 3 × 147

1323 = 3 × 3 × 3 × 49

1323 = 3 × 3 × 3 × 7 × 7

The above can be written as

1323 = 3³ × 7²

Now, 7 is not in triplet. If 7 is in triplet, then derived number will be perfect cube.  

Hence, 1323 must be ‘multiplied by 7’ to get a ‘perfect cube’ as shown below:

1323 = 3³ × 7³ = 21 × 21 × 21 = 9261