Question

find the smallest number which is a perfect square and contains 1620 as a factor?​

Answer 1

Solution :

The given number is 1620

{ We need to prime factorise 1620 to see which of the factor is not doubled or missing one number of the pair. }

Now, 1620

= 2 × 810

= 2 × 2 × 405

= 2 × 2 × 5 × 81

= 2 × 2 × 5 × 3 × 27

= 2 × 2 × 5 × 3 × 3 × 9

= 2 × 2 × 5 × 3 × 3 × 3 × 3

In this term of factors, we see that only 5 is such a number which is not doubled.

So, multiplying 1620 by 5 (which is the required smallest number) will give the perfect square.

• Perfect square is

= 1620 × 5

= 8100

= 90²