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Question
By what numbers should each of the following be divided to get a perfect square? Also, find the number whose square is the new number.
3174
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Solution
3174 = 2 x 3 x 23 x 23
Grouping them into pairs of equal factors:
3174 = 2 x 3 x (23 x 23)
The factors, 2 and 3 are not paired. For a number to be a perfect square, each prime factor has to be paired. Hence, 3174 must be divided by 6 (2 x 3) for it to be a perfect square.
The new number would be (23 x 23).
Hence, the number whose square is the new number is 23.
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