What is the greatest common factor of 25 and 63?

Why not use the Euclidean Algorithm and find out? Divide 63 by 25, and you get a remainder of 13. (The quotient is not important.) Now the divisor of the last division problem becomes the dividend, and the remainder becomes the divisor - that is, we divide 25 by 13 this time. We get a remainder of 12. Divide 13 by 12, and you get a remainder of 1. Divide 12 by 1, you get no remainder. Therefore, this last divisor, 1, is the greatest common factor (or divisor) of the original two numbers. (As a side note, because the gcf is 1, that means those two numbers are what's called relatively prime.)