Question

Find the smallest number which is divided by 8640 to get it a perfect square

Answer 1

Solution :

The given number is 8640

{ We prime factorise the number 8640 and find the number which is not doubled. }

Now, 8640

= 2 × 4320

= 2 × 2 × 2160

= 2 × 2 × 2 × 1080

= 2 × 2 × 2 × 2 × 540

= 2 × 2 × 2 × 2 × 2 × 270

= 2 × 2 × 2 × 2 × 2 × 2 × 135

= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 45

= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 15

= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5

We see that the only unpaired numbers are 3 and 5

Thus, if we divide 8640 by (3 × 5) = 15 (the smallest required number), we will get a perfect square.