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Greatest Common Factor

What is the Greatest Common Factor?

The greatest common factor of two numbers is the largest number that evenly divides both numbers. For example, 221 and 425 have a greatest common factor of 17, because 13*17 = 221, and 17 * 25 = 425.

Euclidean Algorithm

MathJax TeX Test Page This is an algorithm to get you the greatest common factor of two numbers. This is the algorithm: $$gcf(a,b) = gcf(b, a\bmod{}b)$$ $a \bmod b$ is just a better way of saying $a-b$. So, instead of saying $gcf(22, 3) = gcf(19,3) ... gcf(2, 3) = 0$, you could just say $gcf(22, 3) = gcf(3, 2) = 0$

Find the GCF of n! and n! + 3

MathJax TeX Test Page $$gcf(n!, n! + 3) = gcf(n!, 3)$$ So, if $n \geq 3$, the gcf is 3. Otherwise, it's 0.
David Witten

Number of Trailing Zeroes in a Factorial