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Question
Find the smallest number by which the given number must bew multiplied so that the product is a perfect square:
7688
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Solution
Factorise each number into its prime factors.
7688 = 2 x 2 x 2 x 31 x 31
Grouping 7688 into pairs of equal factors:
7688 = (2 x 2) x (31 x 31) x 2
Here, 2 does not occur in pairs. To be a perfect square, every prime factor has to be in pairs. Hence, the smallest number by which 7688 must be multiplied is 2.
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