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All but the square numbers - 53 of them.

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

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

the number is 350 the factors is 175 and 2

Not only can they, but they must. An odd number cannot have an even factor. So none of the factors of either of the two odd numbers can be even and so the GCF is made up of only odd factors and so it must be odd.

1 is the number less than fifty with the fewest number of factors. All other numbers have at least two factors (1, and the integer itself).

360, 420 and 480 each have 24 factors.

Related questions

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).

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.

36

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?

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

The set of positive odd integers.

Five of them.

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

64

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