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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.

60 has many factors. An hour can be divided into 12 times five minutes.
60 has many factors. An hour can be divided into 12 times five minutes.