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Question
Find the smallest number by which the given number must be divided so that the resulting number is a perfect square:
14283
Solution
For each question, factorise the number into its prime factors.
14283 = 3 x 3 x 3 x 23 x 23
Grouping the factors into pairs:
14283 = (3 x 3) x (23 x 23) x 3
Here, the factor 3 does not occur in pairs. To be a perfect square, all the factors have to be in pairs. Hence, the smallest number by which 14283 must be divided for it to be a perfect square is 3.
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