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There are 9 integers less than 100 that have an odd number of factors.

Every factor of a number has a pair, eg 2 & 3 are a factor pair of 6; and so it would be expected that every number has an even number of factors.

However, if the factor pair of a number are the same number (eg 6 & 6 are a factor pair of 36), then there will be an odd number of factors.

When there is a repeated factor like this, the number is a perfect square.

Thus only perfect squares have an odd number of factors.

Less than 100 there are 9 perfect squares (1, 4, 9, 16, 25, 36, 49, 64 & 81) which have an odd number of factors.

100 itself is a perfect square and also has an odd number of factors, but the question asked for those numbers less than 100 with an odd number of factors.

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Q: How many integers less than 100 have an odd number of factors?
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