Q4 of 85 Page 133

Find the smallest number by which 7776 is to be divided to get a perfect square.

Given, a number as 7776. We need to find out a number which if divided by the given number we should get a perfect square.

Step 1: Resolve 7776 into prime factors



We get, 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3


Step 2: Pair the factors obtained


⇒ (2 × 2) × (2 × 2) × (3 × 3) × (3 × 3) × 3 × 2


Step 3: divide the number with the factor which are alone.


Here, 2,3are in pairs and 3,2 are alone.


⇒ 3 × 2 = 6


⇒ = 1296.


Hence, 6 is the smallest number which is to be multiplied to the given number to get perfect square.


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