Best Answer

If "number" is only whole numbers then: 17

If "number" can include fractions, then 1/68

Prime factorising 68 gives:

68 = 22 x 17

For a number to be a square number, all the powers of the primes in the prime factorisation of a number must be even.

68 has two primes:

  • 2 is to the power 2, so already has an even power
  • 17 is to the power 1, so needs to be multiplied by 17 to make it even.

Thus 68 needs to be multiplied by 17 to give 1156 (= 22 x 172) which is 34 (= 2 x 17) squared.

If "number" is not limited to "whole numbers", then 68 x 1/68 = 1 = 12

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Q: What is the smallest number by which you can multiply 68 so that the answer is a square number?
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