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Question

Given that 2940p is a perfect square, write down the smallest possible integer value of p.

Answer

2940 = 2 x 1470
= 2 x 2 x 735
= 2 x 2 x 3 x 245
= 2 x 2 x 3 x 5 x 49
= 2 x 2 x 3 x 5 x 7 x 7

We need two more 2, 1 more 3, and 1 more 5 to make all the factors perfect squares, so…

2 x 2 x 3 x 5 = 60


Check

2940 x 60 = 176,400

22 x 22 x 32 x 52 x 72
= (2 x 2 x 3 x 5 x 7)2
= 4202
= 176,400


 

 

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