# Factors and multiples

A number is a multiple of another number if it is the product of this number with an **integer**.

An integer is a divisor of a number if the ratio of the number with the integer is an **integer**. It is also called a factor.

$$\Tblue{6}$$ is a multiple of $$\Tred{2}$$, $$\Tred{2}$$ is a divisor of $$\Tblue{6}$$, since $$\displaystyle\frac{\Tblue{6}}{\Tred{2}} = 3$$ is an integer.

To rephrase, take two integers $$\Tblue{m}$$ and $$\Tred{d}$$. $$\Tblue{m}$$ is a **multiple** of $$\Tred{d}$$ and $$\Tred{d}$$ is a **divisor** of $$\Tblue{m}$$ if the ratio $$\displaystyle \frac{\Tblue{m}}{\Tred{d}}$$ is an integer.

$$\Tred{4}$$ is a factor of $$\Tblue{12}$$, because $$\displaystyle\frac{12}{\Tred{4}} = 3$$ is an integer

$$\Tred{8}$$ is not a factor of $$\Tblue{12}$$ because $$\displaystyle\frac{12}{\Tred{8}} = 1.5$$ is not an integer.