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 pairArray (row \textbf{×} columns)Product
1 \times 20
Factor Pairs table image 1
20
2 \times 10
Factor Pairs table image 2
20
4 \times 5
Factor Pairs table image 3
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

Factor Pairs image 2 US

10 \times 2 = 20

Factor Pairs image 3 US

The factors of 20 are:

Factor Pairs image 4 US

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.

Factor Pairs image 5 US

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.

Factor Pairs image 6 US

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?

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:

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

[FREE] Factor Pairs Worksheet (Grades 4)

[FREE] Factor Pairs Worksheet (Grades 4)

[FREE] Factor Pairs Worksheet (Grades 4)

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

DOWNLOAD FREE
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[FREE] Factor Pairs Worksheet (Grades 4)

[FREE] Factor Pairs Worksheet (Grades 4)

[FREE] Factor Pairs Worksheet (Grades 4)

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

DOWNLOAD FREE

Factor pairs examples

Example 1: finding factor pairs (even number)

Find the factor pairs of 28.

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

The factor pair is 1 \times 28.

Factor Pairs image 7 US

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

Factor Pairs image 8 US

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.

Factor Pairs image 9 US

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.

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.

Example 3: finding factor pairs (prime number)

Find the factor pairs of 59.

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.

Example 4: finding factor pairs with factors greater than 12

Find the factor pairs of 64.

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.

Example 5: finding factor pairs with factors greater than 12

Find the factor pairs of 66.

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.

Example 6: finding factor pairs (three digit number)

Find the factor pairs of 121.

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.

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

1. Which of the following is a factor pair of 75?

5 \times 15
GCSE Quiz True

2 \times 38
GCSE Quiz False

4 \times 18
GCSE Quiz False

3 \times 24
GCSE Quiz False

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. Which of the following is NOT a factor pair of 56?

2 \times 28
GCSE Quiz False

7 \times 8
GCSE Quiz False

3 \times 15
GCSE Quiz True

4 \times 14
GCSE Quiz False

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

3. Which of the following is a factor pair of 49?

5 \times 9
GCSE Quiz False

7 \times 7
GCSE Quiz True

2 \times 24
GCSE Quiz False

3 \times 16
GCSE Quiz False

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

4. Which of the following is NOT a factor pair of 88?

2 \times 44
GCSE Quiz False

4 \times 22
GCSE Quiz False

8 \times 11
GCSE Quiz False

3 \times 29
GCSE Quiz True

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

5. Which of the following is a factor pair of 95?

9 \times 10
GCSE Quiz False

5 \times 19
GCSE Quiz True

4 \times 23
GCSE Quiz False

6 \times 15
GCSE Quiz False

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

6. Which of the following is NOT a factor pair for 60?

2 \times 30
GCSE Quiz False

4 \times 15
GCSE Quiz False

5 \times 14
GCSE Quiz True

6 \times 10
GCSE Quiz False

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.

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