No. For example:
3 is a factor of 9, 15, 21, ...
3 is not a factor of 5, 7, 11, 13, 17, 19, ...
Note that there are lots of odd numbers that have NO smaller factors (excluding 1, and negative factors, of course). Such numbers are called prime numbers. The sequence of prime numbers starts with:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...
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All odd numbers have odd factors.
25 is an odd factor of 100.
An odd number
you get an odd number
The result is an odd number.