2.4 Find multiples and factors  (Page 10/9)

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.