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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:
1800
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Solution
For question, factorise the number into its prime factor.
1800= 2 x 2 x 2 x 3 x 3 x 5 x 5
Grouping the factors into pairs:
1800 = (2 x 2) x (3 x 3) x (5 x 5) x 2
Here, the factor 2 does not occur in pairs. To be a perfect square, all the factors have to be in pairs. Hence, the smallest number by which 1800 must be divided for it to be a perfect square is 2.
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