Multiples

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Multiples

Here you will learn about multiples, including how to calculate multiples of a number and solve problems using knowledge of multiples.

Students will first learn about multiples as part of operations and algebraic thinking in elementary school.

What are multiples?

Multiples are the products you get when two numbers, or factors, are multiplied.

For example, the first five multiples of $katex is not defined$ are $katex is not defined$ , $katex is not defined$ , $katex is not defined$ , $katex is not defined$ , and $katex is not defined$ .

You can skip count on a number line to find multiples of $katex is not defined$ .

The number line shows the first $katex is not defined$ multiples of $katex is not defined$ , but you could keep skipping counting to find more multiples.

To make them easier to find, multiples of the numbers $katex is not defined$ to $katex is not defined$ have patterns. They can help you decide if a given number is a multiple of $katex is not defined$ to $katex is not defined$ .

Number	Multiples	Pattern
$katex is not defined$	$katex is not defined$	every number is a multiple of $katex is not defined$
$katex is not defined$	$katex is not defined$	the last digit is an even number
$katex is not defined$	$katex is not defined$	the sum of the digits is divisible by three
$katex is not defined$	$katex is not defined$	the number is double of a multiple of $katex is not defined$
$katex is not defined$	$katex is not defined$	the last digit is zero or five
$katex is not defined$	$katex is not defined$	the number is divisible by both two and three
$katex is not defined$	$katex is not defined$	*No divisibility pattern
$katex is not defined$	$katex is not defined$	the number is double a multiple of $katex is not defined$
$katex is not defined$	$katex is not defined$	the sum of the digits is divisible by nine
$katex is not defined$	$katex is not defined$	the last digit is zero

What are multiples?

Common Core State Standards

How does this relate to 4th grade math?

4th Grade: Operations and Algebraic Thinking (4.OA.B.4)
Determine whether a given whole number in the range $katex is not defined$ to $katex is not defined$ is a multiple of a given one-digit number.

How to identify multiples

In order to find if a number is a multiple of another number:

Think about the pattern for the multiples of the number.
Decide if the number is a multiple.

[FREE] Multiples Worksheet (Grade 4)

Use this worksheet to check your grade 4 students’ understanding of multiples. 15 questions with answers to identify areas of strength and support!

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[FREE] Multiples Worksheet (Grade 4)

Use this worksheet to check your grade 4 students’ understanding of multiples. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREE

Multiples examples

Example 1: decide whether a number is a multiple

Is $katex is not defined$ a multiple of $katex is not defined$ ?

Think about the pattern for the multiples of the number.

Start a list of multiples for $katex is not defined$ :

$katex is not defined$ , $katex is not defined$ , $katex is not defined$ , $katex is not defined$ , $katex is not defined$ …

Notice that the multiples of $katex is not defined$ are also multiples of $katex is not defined$ and $katex is not defined$ .

This pattern is true for all multiples of $katex is not defined$ .

2Decide if the number is a multiple.

✔ The last digit $katex is not defined$ is even, so it is a multiple of $katex is not defined$ .

✘ The sum of the digits $katex is not defined$ , so it is not a multiple of $katex is not defined$ .

$katex is not defined$ is NOT a multiple of $katex is not defined$ because it is NOT a multiple of $katex is not defined$ .

Skip counting on a number line shows that $katex is not defined$ is NOT a multiple of $katex is not defined$ .

Example 2: decide whether a number is a multiple

Is $katex is not defined$ a multiple of $katex is not defined$ ?

Think about the pattern for the multiples of the number.

Show step

Start a list of multiples for $katex is not defined$ :

$katex is not defined$ , $katex is not defined$ , $katex is not defined$ , $katex is not defined$ , $katex is not defined$ …

Notice that they end in either a $katex is not defined$ or a $katex is not defined$ .

This pattern is true for all multiples of $katex is not defined$ .

Decide if the number is a multiple.

Show step

✔ $katex is not defined$ is a multiple of $katex is not defined$ because it ends in a $katex is not defined$ .

Skip counting on a number line shows that $katex is not defined$ is the $katex is not defined$ multiple of $katex is not defined$ .

Example 3: decide whether a number is a multiple

Is $katex is not defined$ a multiple of $katex is not defined$ ?

Think about the pattern for the multiples of the number.

Show step

Start a list of multiples for $katex is not defined$ :

$katex is not defined$ , $katex is not defined$ , $katex is not defined$ , $katex is not defined$ , $katex is not defined$ …

Notice that they are all doubles of a multiple of $katex is not defined$ .

This pattern is true for all multiples of $katex is not defined$ .

Decide if the number is a multiple.

Show step

✘ $katex is not defined$ is the double of $katex is not defined$ , but $katex is not defined$ is not a multiple of $katex is not defined$ .

$katex is not defined$ is not a multiple of $katex is not defined$ because it is not a double of a multiple of $katex is not defined$ .

Skip counting on a number line shows that $katex is not defined$ is NOT a multiple of $katex is not defined$ .

Example 4: decide whether a number is a multiple

Is $katex is not defined$ a multiple of $katex is not defined$ ?

Think about the pattern for the multiples of the number.

Show step

Start a list of multiples for $katex is not defined$ :

$katex is not defined$ , $katex is not defined$ , $katex is not defined$ , $katex is not defined$ , $katex is not defined$ …

Notice that the sum of the digits is divisible by $katex is not defined$ .

This pattern is true for all multiples of $katex is not defined$ .

Decide if the number is a multiple.

Show step

✔ $katex is not defined$ is a multiple of $katex is not defined$ , because the sum of the digits $katex is not defined$ is divisible by $katex is not defined$ .

Skip counting on a number line shows that $katex is not defined$ is the eighth multiple of $katex is not defined$ .

Example 5: decide whether a number is a multiple

Is $katex is not defined$ a multiple of $katex is not defined$ ?

Think about the pattern for the multiples of the number.

Show step

Start a list of multiples for $katex is not defined$ :

$katex is not defined$ , $katex is not defined$ , $katex is not defined$ , $katex is not defined$ , $katex is not defined$ …

Notice that the sum of the digits is divisible by $katex is not defined$ .

This pattern is true for all multiples of $katex is not defined$ .

Decide if the number is a multiple.

Show step

✔ $katex is not defined$ is a multiple of $katex is not defined$ , because the sum of the digits $katex is not defined$ is divisible by $katex is not defined$ .

Skip counting on a number line shows that $katex is not defined$ is the $katex is not defined$ multiple of $katex is not defined$ .

Example 6: decide whether a number is a multiple

An elementary school is performing a play. They want to put out $katex is not defined$ chairs for the audience. If they want the same amount of chairs in each row, should they do rows of $katex is not defined$ , $katex is not defined$ or $katex is not defined$ ?

Think about the pattern for the multiples of the number.

Show step

Multiples of $katex is not defined$ : the sum of the digits is divisible by three.

Multiples of $katex is not defined$ : the number is double a multiple of $katex is not defined$ .

Multiples of $katex is not defined$ : the last digit is zero.

Decide if the number is a multiple.

Show step

✘ $katex is not defined$ is NOT a multiple of $katex is not defined$ , because the sum of the digits $katex is not defined$ is NOT divisible by $katex is not defined$ .

✔ $katex is not defined$ is a multiple of $katex is not defined$ , because it is double a multiple of $katex is not defined$ .

The school should put the $katex is not defined$ chairs in rows of $katex is not defined$ .

Teaching tips for multiples

Use a multiplication table so that students can see examples of multiples and look for patterns.

While students will need to remember the multiple patterns to solve quickly, avoid just using math worksheets. Help students deepen their understanding and likelihood of remembering by also doing hands-on activities. For example, give students $katex is not defined$ counters and ask them to make as many arrays as possible to find out what factors $katex is not defined$ is a multiple of.

Play games regularly to help students memorize larger multiples. For example, have students count starting from $katex is not defined$ (the first student says $katex is not defined$ , the second says $katex is not defined$ , the third says $katex is not defined$ and so on), but challenge them to use a different word for a certain multiple each time. So if they were playing with multiples of $katex is not defined$ , whenever a student got to a multiple of $katex is not defined$ , they would say “cookie” instead of the multiple.

Easy mistakes to make

Confusing the terms multiples and factors
Factors and multiples are easily mixed up. Remember multiples are the numbers in the middle of the multiplication table, whereas factors are the numbers around the outside (the numbers being multiplied).

Forgetting the number itself as a multiple
All numbers are a multiple of themselves.
For example, the multiples of $katex is not defined$ are: $katex is not defined$ , $katex is not defined$ , $katex is not defined$ , $katex is not defined$ and so on and so $katex is not defined$ is a multiple of itself.

Practice multiples questions

katex is not defined

katex is not defined

katex is not defined

katex is not defined

For multiples of $katex is not defined$ , the last digit is an even number. $katex is not defined$ ends in an even number and $katex is not defined$ , so $katex is not defined$ is a multiple of $katex is not defined$ .

katex is not defined

katex is not defined

katex is not defined

katex is not defined

Using a number line to skip count by $katex is not defined$ , shows that $katex is not defined$ is a multiple of $katex is not defined$ .

katex is not defined

katex is not defined

katex is not defined

katex is not defined

For multiples of $katex is not defined$ , the sum of the digits is divisble by three. $katex is not defined$ is not divisible by $katex is not defined$ , so $katex is not defined$ is NOT a multiple of $katex is not defined$ .

katex is not defined

katex is not defined

katex is not defined

katex is not defined

For multiples of $katex is not defined$ , the number is double a multiple of $katex is not defined$ . $katex is not defined$ is the double of $katex is not defined$ , so $katex is not defined$ is NOT a multiple of $katex is not defined$ .

$katex is not defined$ boxes

For multiples of $katex is not defined$ , the number is divisible by both two and three. $katex is not defined$ is a multiple of $katex is not defined$ , because it ends in an even number $katex is not defined$ .
$katex is not defined$ is a multiple of $katex is not defined$ , because $katex is not defined$ and $katex is not defined$ .

So $katex is not defined$ is a multiple of $katex is not defined$
The grocery store can put $katex is not defined$ boxes on each shelf.

Multiples FAQs

What is the difference between multiples and times tables?

Times tables are a list of multiplication equations for a certain number and include both factors and multiples. Multiples are the answers (products) in times tables.

Can I use division to find multiples?

Yes, if a number divides another number without a remainder, it’s a multiple. For example, in the question “is $katex is not defined$ a multiple of $katex is not defined$ ?” you can solve $katex is not defined$ . There are no remainders, so it is a multiple.

Do negative numbers have multiples?

All positive and negative numbers have multiples. However, in 4th grade math you only work with positive numbers.

Do prime numbers have multiples?

Prime numbers have an infinite amount of multiples but only $katex is not defined$ factors.

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