The positive integer factors of 36 are:
1, 2, 3, 4, 6, 9, 12, 18, 36
Of these, 1, 3, and 9 are odd.
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That number is 36.
These numbers between 1 and 40 have an odd number of factors: 4, 9, 16, 25, 36.
Since any odd number can be a factor, there is an infinite amount of them.
The number 1,980 has 36 factors.
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.