What number between 1 and 100 has only even factors?

Answer 1

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