A common factor of 100 and 25 is 25. 25 goes into both 100 and 25. A good way to check other numbers is divide the larger number by the smaller number. If you have 10 and 25, that won't work, so you will have to find numbers that go into both. An easy way to do this is find different ways to get each number.
Example:
2x5=10
5x5=25
5 goes into each number at least one time, so it is a common factor.
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The greatest common factor of 15 and 105 is 15.
The GCF is 15.
Since 15 is a factor of 60, it is automatically the GCF.
Since 5 is a factor of 15, it is automatically the greatest common factor of the pair.
The GCF is 1.