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Q: How many integers less than 60 have an even number of factors?

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There are 44 positive integers less than 2,010 that have an odd number of factors.

There are 1,963 such integers. Every factor of a number has a pair. The only time there will be an odd number of factors is if one factor is repeated, ie the number is a perfect square. So the question is really asking: how many positive integers less than 2008 (in the range 1 to 2007) are not perfect squares. √2007 = 44 and a bit (it lies between 44 and 45) So there are 44 integers less than (or equal to) 2007 which are perfect squares → 2007 - 44 = 1963 integers are not perfect squares in the range 1-2007 and have an even number of factors (divisors).

36

The number is 54. It is greater than 36 and less than 70. One of its factors is 9 and it is an even number.

There are four odd numbers less that 100 that have 6 factor. This does not compare with even numbers that have 12 factors!

When one of the integers is negative and the other is not.

When one of the integers is negative and the other is not.

The concept of the number of factors is appropriate only with positive integers. Otherwise, if p is a factor of the given number n, do you also count -p? That would double the number of factors. So are there 3 factors or 6?

The set of positive odd integers.

64

10, 8, 6, 4, 2, 0 and all the negative even integers.

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.

Five of them.

32

There are 17.

Two integers A and B are graphed on a number line. If A is less than B is A always less than B?

That happens when only one of the two integers is negative.

Probably because that's more or less the definition of "rational number": a number that can be expressed as a ratio of integers.

23 of them.

There is no such number.

Perfect squares have odd numbers of factors. The perfect squares less than 100 are: 1,4,9,16,25,36,49,64,81,100. 64 seems to fit both criteria.

201

The four even integers are 6, 8, 10, 12. 6 x 8 = 48 10 x 12 = 120 120 - 48 = 72

There are infinitely many of them: all integers which are less than 24.

The least common factor of any set of integers is 1.