What is the common factors?

A divisor is an integer greater than or equal to 1 and less than or equal to the number itself that is divisible by some positive integer.

For example, the divisors of 12 are 1,2,3,4,6,12.

Common factors are divisors that are common to two or more numbers.

As an example, consider the common factors of 12 and 18.

The divisors of 12 and 18 are as follows

\begin{align} \text{Divisors of }12\text{ : }&1,2,3,4,6,12\notag\\ \text{Divisors of }18\text{ : }&1,2,3,6,9,18\notag \end{align}

Thus, we see that the common factors of 12 and 18 are 1, 2, 3, and 6.

Example

Example 1

Find the common factors of 4 and 8.

Solution

\begin{align} \text{Divisors of }4\text{ : }&1,2,4\notag\\ \text{Divisors of }8\text{ : }&1,2,4,8\notag \end{align}

Thus, the common factors of 4 and 8 are 1,2,4.

Example 2

Find the common factors of 80 and 100.

Solution

\( \text{Divisors of }80\text{:} \)

\[ 1,2,4,5,8,10,16,20,40,80 \]

\( \text{Divisors of }100\text{:} \)

\[ 1,2,4,5,10,20,25,50,100 \]

Thus, the common factors of 80 and 100 are 1,2,4,5,10,20.