Question

Find the least number by which 31752 must be divided so as to get a perfect square. Also, find the square root of the resulting number.

Answer 1

Solution :-

To find the least number by 31752 should be divided so that the resulting 

number becomes a perfect square, we have to find the prime factorization of 31752

 

Prime factorization of 31752

       ___________

  2  |  31752

      |___________  

  2  |  15876

      |___________

  2  |   7938

      |___________

  3  |   3969

      |___________

  3  |    1323

      |___________

  3  |     441

      |___________

  3  |       147

      l___________

  7  l      49

      l___________

  7  l      7

      l___________

  7  l      1

      l___________

Prime factorization of 31752 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 7 x 7 x 7

We can see that only 2 and 7 are unpaired.

So, 2 x 7 = 14, is the least number should be divided so that the resulting

number is a perfect square.

Let us check it.

31752 ÷ 14 = 2268

√2268 = 47

Hence proved.

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