2.4 Find multiples and factors

Identify multiples of numbers

Annie is counting the shoes in her closet. The shoes are matched in pairs, so she doesn’t have to count each one. She counts by twos: $2,4,6,8,10,12.$ She has $12$ shoes in her closet.

The numbers $2,4,6,8,10,12$ are called multiples of $2.$ Multiples of $2$ can be written as the product of a counting number and $2.$ The first six multiples of $2$ are given below.

A multiple of a number    is the product of the number and a counting number. So a multiple of $3$ would be the product of a counting number and $3.$ Below are the first six multiples of $3.$

We can find the multiples of any number by continuing this process. [link] shows the multiples of $2$ through $9$ for the first twelve counting numbers.

Recognizing the patterns for multiples of $2,5,10,\text{and}3$ will be helpful to you as you continue in this course.

[link] shows the counting numbers from $1$ to $50.$ Multiples of $2$ are highlighted. Do you notice a pattern?

The last digit of each highlighted number in [link] is either $0,2,4,6,\text{or}8.$ This is true for the product of $2$ and any counting number. So, to tell if any number is a multiple of $2$ look at the last digit. If it is $0,2,4,6,\text{or}8,$ then the number is a multiple of $2.$

Now let’s look at multiples of $5.$ [link] highlights all of the multiples of $5$ between $1$ and $50.$ What do you notice about the multiples of $5?$

All multiples of $5$ end with either $5$ or $0.$ Just like we identify multiples of $2$ by looking at the last digit, we can identify multiples of $5$ by looking at the last digit.