Question

How do you find the greatest common factor ($\text{GCF}$) of two numbers?

Answer 1

Find the Greatest Common Factor of the two numbers:

The Greatest Common factor is the largest factor of two or more numbers that exactly divides the given two or more numbers.

Example:

Consider the two numbers $216$ and $360$.

$216=2\times 2\times 2\times 3\times 3\times 3$

$360=2\times 2\times 2\times 3\times 3\times 5$

Here, $2,2,2,3,3$are the common factors of $216$ and $360$.

Thus multiplying the common factors gives the greatest factor of $216$ and $360$.

$\Rightarrow 2\times 2\times 2\times 3\times 3=72$

$72$ is the Greatest Common Factor of $216$ and $360$.

Hence this method is used to find the Greatest Common Factor of any two numbers.