Factor Pairs - Elementary Math Steps, Examples & Questions

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Multiplication and division within 100

Factors

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Factor pairs

Here you will learn about factor pairs, including how to find factor pairs for a given number.

Students will first learn about factor pairs as a part of operations and algebraic thinking in 4th grade.

What are factor pairs?

Factor pairs are two numbers that are multiplied to create a particular product.

Numbers can have more than one factor pair.

All numbers have the factor of $1,$ therefore the first factor pair will always be $1 \, \times$ the given number.

For example, $1$ and $20, \; 2$ and $10,$ and $4$ and $5$ are factor pairs for $20.$

Factor pair	Array (row $\textbf{×}$ columns)	Product
$1 \times 20$		$20$
$2 \times 10$		$20$
$4 \times 5$		$20$

Factor pairs have a commutative property, which means you can switch the order and the product is the same.

For example,

$2 \times 10 = 20$

$10 \times 2 = 20$

The factors of $20$ are:

Factors are numbers that multiply together to find a product. They will divide into a whole number with no remainder and can sometimes be called divisors.

Multiplication charts can help you identify factors.

For example, on the multiplication chart below, you can see that $2$ and $10,$ and $4$ and $5$ are factors of $20.$

Factors can be prime or composite.

Composite numbers are numbers with more than two factors and prime numbers are numbers with exactly two factors, themselves and $1.$

For smaller numbers, being familiar with your multiplication facts will help you find all factor pairs. For larger numbers, being familiar with divisibility rules will help you find all the factor pairs.

You can use factor pairs to help find common denominators, calculate areas, and will help you with algebraic expressions in middle school.

What are factor pairs?

Common Core State Standards

How does this relate to 4th grade math?

Grade 4: Operations and Algebraic Thinking (4.OA.B.4)
Find all factor pairs for a whole number in the range $1-100.$ Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range $1-100$ is a multiple of a given one-digit number. Determine whether a given whole number in the range $1-100$ is prime or composite.

How to find factor pairs of a number

In order to find factor pairs of a number, you need to:

State the pair $\bf{1 \, \times }$ the number.
Find the next smallest factor of the number and calculate its factor pair.
Repeat until the next factor pair is the same as the previous pair.
Write out the list of factor pairs for the given number.

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$[FREE] End of Year Math Assessments (Grade 4 & Grade 5)$

[FREE] End of Year Math Assessments (Grade 4 & Grade 5)

$[FREE] End of Year Math Assessments (Grade 4 & Grade 5)$

Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!

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Factor pairs examples

Example 1: finding factor pairs (even number)

Find the factor pairs of $28.$

State the pair $\bf{1 \, \times }$ the number.

The factor pair is $1 \times 28.$

2Find the next smallest factor of the number and calculate its factor pair.

$28$ is an even number, so $2$ will be a factor of $28.$

$28 \div 2=14$

So the next factor pair is,

$2 \times 14$

3Repeat until the next factor pair is the same as the previous pair.

$28$ is not divisible by $3$ or $9$ because the sum of its digits, $2+8=10,$ is not divisible by $3.$

$28 \div 4=7,$ so the next factor pair is $4 \times 7.$

$28$ is not divisible by $5$ because it does not end in a $0$ or $5.$

$28$ is not divisible by $6$ because it is not divisible by $3.$

The next factor to try is $7.$ As factors are communicative, $4 \times 7=7 \times 4,$ which is the same as the previous factor pair.

All of the factor pairs have been found.

4Write out the list of factor pairs for the given number.

The number $28$ has three factor pairs:

$\begin{aligned} & 1 \times 28 \\\\ & 2 \times 14 \\\\ & 4 \times 7 \end{aligned}$

Example 2: finding factor pairs (odd number)

Find the factor pairs of $35.$

State the pair $\bf{1 \, \times }$ the number.

The factor pair is $1 \times 35.$

Find the next smallest factor of the number and calculate its factor pair.

$35$ is not an even number, so it is not divisible by $2$ or $4.$

$35$ is not divisible by $3$ or $9$ because the sum of its digits, $3 + 5 = 8,$ is not divisible by $3.$

$35 \div 5=7$

So the next factor pair is,

$5 \times 7$

Repeat until the next factor pair is the same as the previous pair.

$35$ is not divisible by $6,$ because $35$ is not divisible by $2$ or $3.$

The next factor to try is $7.$ As factors are communicative, $5 \times 7=7 \times 5,$ which is the same as the previous factor pair.

All of the factor pairs have been found.

Write out the list of factor pairs for the given number.

The number $35$ has two factor pairs:

$\begin{aligned} & 1 \times 35 \\\\ & 5 \times 7 \end{aligned}$

Example 3: finding factor pairs (prime number)

Find the factor pairs of $59.$

State the pair $\bf{1 \, \times }$ the number.

The factor pair is $1 \times 59.$

Find the next smallest factor of the number and calculate its factor pair.

$59$ is not divisible by $2$ or $4$ because the last digit isn’t even.

$59$ is not divisible by $3$ or $9$ because the sum of the digits, $5+9=14,$ is not divisible by $3.$

$59$ is not divisible by $5$ because the last digit is not a $0$ or $5.$

$59$ is not divisible by $6$ because the number is not divisible by $2$ or $3.$

$59$ is not divisible by $7$ or $8$ because $59 \div 7$ and $59 \div 8$ have remainders, and are not divided evenly.

$59$ does not have any other factors besides $1$ or itself. $59$ is a prime number.

Repeat until the next factor pair is the same as the previous pair.

The only factors of $59$ are $1$ and itself.

Write out the list of factor pairs for the given number.

The number $59$ only has one factor pair:

$1 \times 59$

Example 4: finding factor pairs with factors greater than 12

Find the factor pairs of $64.$

State the pair $\bf{1 \, \times }$ the number.

The factor pair is $1 \times 64.$

Find the next smallest factor of the number and calculate its factor pair.

$64$ ends in a $4,$ an even number, so $2$ will be a factor of $64.$

$64 \div 2=32$

So the next factor pair is,

$2 \times 32$

Repeat until the next factor pair is the same as the previous pair.

$64$ is not divisible by $3$ or $9$ because the sum of the digits, $6 + 4 = 10,$ is not divisible by $3.$

$64$ is divisible by $4,$ because $64 \div 4=16$

So the next factor pair is, $4 \times 16.$

$64$ is not divisible by $5$ because the last digit is not a $0$ or $5.$

$64$ is not divisible by $6$ because the number is not divisible by $2$ or $3.$

$64$ is not divisible by $7$ because $64 \div 7$ has a remainder, and is not divided evenly.

$64$ is divisible by $8,$ because $64 \div 8=8$

So the next factor pair is, $8 \times 8.$

The factors began repeating each other, therefore, all factor pairs have been found.

Write out the list of factor pairs for the given number.

The number $64$ has $4$ factor pairs:

$\begin{aligned} & 1 \times 64 \\\\ & 2 \times 32 \\\\ & 4 \times 16 \\\\ & 8 \times 8 \end{aligned}$

Example 5: finding factor pairs with factors greater than 12

Find the factor pairs of $66.$

State the pair $\bf{1 \, \times }$ the number.

The factor pair is $1 \times 66.$

Find the next smallest factor of the number and calculate its factor pair.

$66$ ends in a $6,$ an even number, so $2$ will be a factor of $66.$

$66 \div 2=33$

The next factor pair is $2 \times 33.$

Repeat until the next factor pair is the same as the previous pair.

$66$ is divisible by $3,$ because the sum of its digits, $6+6=12,$ is divisible by $3.$

$66 \div 3=22$

The next factor pair will be $3 \times 22.$

$66$ is not divisible by $4,$ because $66 \div 4$ has a remainder, and is not divided evenly.

$66$ is not divisible by $5,$ because the last digit is not a $0$ or $5.$

$66$ is divisible by $6,$ because it is divisible by both $2$ and $3.$

$66 \div 6=11$

The next factor pair will be $6 \times 11.$

$66$ is not divisible by $7$ or $8,$ because $66 \div 7$ and $66 \div 8$ have remainders, and are not divided evenly.

$66$ is not divisible by $9,$ because the sum of its digits, $6+6=12,$ is not divisible by $9.$

All factor pairs have been found.

Write out the list of factor pairs for the given number.

The number $66$ has $4$ factor pairs:

$\begin{aligned} & 1 \times 66 \\\\ & 2 \times 33 \\\\ & 3 \times 22 \\\\ & 6 \times 11 \end{aligned}$

Example 6: finding factor pairs (three digit number)

Find the factor pairs of $121.$

State the pair $\bf{1 \, \times }$ the number.

The factor pair is $1 \times 121.$

Find the next smallest factor of the number and calculate its factor pair.

$121$ is not divisible by $2$ or $4$ because the last digit isn’t even.

$121$ is not divisible by $3$ or $9$ because the sum of the digits, $1 + 2 +1 = 4,$ is not divisible by $3.$

$121$ is not divisible by $5$ because the last digit is not a $0$ or $5.$

$121$ is not divisible by $6$ because the number is not divisible by $2$ or $3.$

$121$ is not divisible by $7$ or $8$ because $89 \div 7$ and $89 \div 8$ have remainders, and are not divided evenly.

$121$ is not divisible by $10$ because it does not end in a zero.

$121$ is divisible by $11,$ because $121 \div 11 = 11.$

Repeat until the next factor pair is the same as the previous pair.

All factor pairs have been found.

Write out the list of factor pairs for the given number.

The number $121$ has two factor pairs:

$\begin{aligned} & 1 \times 121 \\\\ & 11 \times 11 \end{aligned}$

Teaching tips for factor pairs

Using some type of visual model is a great way to introduce factor pairs. Students should be familiar with arrays by this grade level and can help students organize the positive factors.

While worksheets and assigning as math homework are an easy way to provide students practice with factor pairs, when students are first working with them, providing hands-on practice, like manipulatives, will help students cement the learning.

Easy mistakes to make

Confusing factors and multiples
Factors are two numbers multiplied together to get a product, like $6 \times 7 = 42.$
Multiples are the products of factors, like the multiples of $4$ are $4, 8, 12, 16.$

Remember $\bf{1}$ and the number itself are factors
All numbers have a factor of $1,$ and all numbers are a factor of themselves. For example, the factors of $4$ are: $1, 2,$ and $4.$

Practice factor pairs questions

5 \times 15

2 \times 38

4 \times 18

3 \times 24

You can use divisibility rules to determine which of the answer choices is a factor pair of $75.$

$75$ is not divisible by $2$ because the last digit is not even or a $0.$
$75$ is not divisible by $3$ because the sum of the digits, $7+5=13,$ is not divisible by $3.$
$75$ is not divisible by $4$ because $75 \div 4,$ gives you a remainder.
$75$ is divisible by $5$ because the last digit is $5.$

The factor pairs for $75$ are:

Factor Pairs image 22 US

2 \times 28

7 \times 8

3 \times 15

4 \times 14

You can use divisibility rules to determine which of the answer choices is NOT a factor pair of $56.$

$56$ is divisible by $2$ because $6$ is an even number.
$56$ is not divisible by $3$ because the sum of the digits, $5+6=11,$ is not divisible by $3.$
$56$ is not divisible by $4$ because $56 \div 4,$ gives you a remainder.
$56$ is not divisible by $7$ because $56 \div 7,$ gives you a remainder.

The factor pairs for $56$ are:

Factor Pairs image 23 US

5 \times 9

7 \times 7

2 \times 24

3 \times 16

You can use divisibility rules to determine which of the answer choices is a factor pair of $49.$

$49$ is not divisible by $2$ because $9$ is not an even number or zero.
$49$ is not divisible by $3$ because the sum of the digits, $4+9=13,$ is not divisible by $3.$
$49$ is not divisible by $5$ because the last digit is not $0$ or $5.$
$49$ is not divisible by $7$ because $49 \div 7,$ gives you a remainder.

The factor pairs for $49$ are:

Factor Pairs image 24 US

2 \times 44

4 \times 22

8 \times 11

3 \times 29

You can use divisibility rules to determine which of the answer choices is NOT a factor pair of $88.$

$88$ is divisible by $2$ because $8$ is an even number.
$88$ is not divisible by $3$ because the sum of the digits, $8+8=16,$ is not divisible by $3.$
$88$ is divisible by $4$ because $88 \div 4 = 22.$
$88$ is divisible by $8$ because $88 \div 8 = 11.$

The factor pairs for $88$ are:

Factor Pairs image 25 US

9 \times 10

5 \times 19

4 \times 23

6 \times 15

You can use divisibility rules to determine which of the answer choices is a factor pair of $95.$

$95$ is not divisible by $4$ because $95 \div 4$ gives you a remainder.
$95$ is divisible by $5$ because it ends with $5.$
$95$ is not divisible by $6$ because it is not divisible by $2$ or $3.$
$95$ is not divisible by $9$ because the sum of the digits, $9+5=14,$ is not divisible by $9.$

The factor pairs for $95$ are:

Factor Pairs image 26 US

2 \times 30

4 \times 15

5 \times 14

6 \times 10

You can use divisibility rules to determine which of the answer choices is NOT a factor pair of $60.$

$60$ is divisible by $2$ because the last digit is $0.$
$60$ is not divisible by $4$ because $60 \div 4$ gives you a remainder.
$60$ is divisible by $5$ because it ends with $0.$
$60$ is divisible by $6$ because it is divisible by $2$ and $3.$

The factor pairs for $60$ are:

Factor Pairs image 27 US

Factor pairs FAQs

Can factor pairs only contain positive numbers?

No, factors or negative numbers can be negative numbers as well. However, in elementary school students will only work with positive numbers.

How else will I use factor pairs?

Factor pairs will be used to help find the common denominators, including the greatest common factor, or GCF.

The next lessons are

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