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When we talk about a number with only even factors, we consider only the prime factors, as an even composite factor can still have an odd prime factor. For example, 12 can be factorized with only even factors (6*2), but because 6 = 2*3, there is still a hidden odd factor.

Now, consider the fact that the only even Prime number is two. Therefore, if a number has prime factors other than two, it will have odd factors. It is easy to see therefore that the only numbers with entirely even factors are powers of two. Excluding 2^0 = 1, the powers of two between 1 and 100 are:
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64

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Q: What number between 1 and 100 has only even factors?
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What even number that have only have two factors?

2 is an even number with only 2 factors.


What even number has only 2 factors?

2 is the only positive even number with only 2 positive integer factors. (1 and 2 are the factors. )


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Do only square numbers have an even number of factors?

No, only square numbers have an odd number of factors.


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None of them. Even numbers are divisible by themselves and 2. Every even number greater than two has at least two even factors..


Is the gcf of an odd and even number always even?

No. The opposite is true: the gcf of an odd number and an even number is always odd. All the factors of an odd number are odd; or to put it another way: If a number has an even factor, the number itself must be even. Thus the only common factors between odd and even numbers must be odd.


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