Learn the definition of factor pairs and about the product of two factors. Using examples, understand the difference between a factor and a multiple.
Updated: 12/12/2021
Factors & Products
Definition of Factor Pairs
 |
There are many ways to count how many tiles there are in the picture, but since the tiles are arranged in an array, an equal number in each row, the most efficient way to count them is with multiplication. There are 3 rows with 3 tiles in each row. Each 3 represents a factor. To find the total, multiply the factor pairs 3 and 3, which equals 9 tiles in all. Factors are numbers multiplied to result in a total. Since a pair refers to two items, a factor pair is two factors.
Product of Two Factors
When two numbers are multiplied, the answer they produce is called the product. In the tile example, 3 x 3 = 9. The product of 3 x 3 is 9 and 9 is divisible by 3.
 |
The order of the factor pairs in a multiplication equation does not change the product. Factors can be multiplied forward and backward.
Examples of Factor Pairs
Products can have more than one factor pair. For example, the number 6 has two factor pairs because 6 can be composed in different ways. The following arrays show various ways to make 6. The numbers of rows and columns are factors.
 |
 |
The factors of 6 can be expressed in a list as 1, 2, 3, and 6 or as pairs 1 and 6 and 2 and 3. Since multiplication is commutative, the same forward and backward, it is not necessary to repeat factor pairs in reverse order. If 2 and 3 are a factor pair of 6, it is assumed that 3 and 2 are also a factor pair of 6.
Another number with more than one factor pair is 24. To find factor pairs for 24, think about the ways 24 can be divided evenly without remainders.
{eq}24 \div 6 = 4 {/eq} and {eq}24 \div 4 = 6 {/eq}
{eq}24 \div 2 = 12 {/eq} and {eq}24 \div 12 = 2 {/eq}
{eq}24 \div 3 = 8 {/eq} and {eq}24 \div 8 = 3 {/eq}
{eq}24 \div 1 = 24 {/eq} and {eq}24 \div 24 = 1 {/eq}
So, the factor pairs for 24 are 1 and 24, 2 and 12, 6 and 4, and 3 and 8. Or, listed out the factors of 24 are 1, 2, 3, 4, 6, 8, and 12.
Here are a few more factor pairs.
15: 1 and 15, 3 and 5
20: 1 and 20, 2 and 10, 4 and 5
27: 1 and 27, 3 and 9
Definition of a Factor Pair
Let's say a mother in your neighborhood hires you to babysit for $75 a night, and you can babysit four nights of the week. Of course, to figure out your weekly income, we would multiply the nightly income by the number of nights you can work:
75 * 4 = 300
You'll make $300 in one week! Not bad.
Factors are the numbers you multiply together. In this multiplication sentence, 75 and 4 are the factors. 300 is the product, which is the answer we get when we multiply two factors together.
So, in this multiplication sequence, 3 * 4 = 12, 3 and 4 are the factors, and 12 is the product.
You must cCreate an account to continue watching
Register to view this lesson
Are you a student or a teacher?
Create Your Account To Continue Watching
As a member, you'll also get unlimited access to over 84,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.
Get unlimited access to over 84,000 lessons.
Try it now
It only takes a few minutes to setup and you can cancel any time.
Already registered? Log in here for access
BackResources created by teachers for teachers
Over 30,000 video lessons
& teaching resources‐all
in one place.
I would definitely recommend Study.com to my colleagues. It’s like a teacher waved a magic wand and did the work for me. I feel like it’s a lifeline.
Jennifer B.
Teacher
Back
Your next lesson will play in
10 seconds
What is the Difference Between a Factor and a Multiple?
Factors are numbers that are multiplied with each other, and the answer that results is the product. Another way to describe the product of two factors is to say it is a multiple of a number. Is 9 a multiple of 3? Yes! 9 is a multiple of 3 because when the factors 3 and 3 are multiplied, 9 is the product. Skip-counting by 3 is also a way to find out its multiples- 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39... are all multiples of 3. They are products of 3 multiplied by another factor.
Is 17 a multiple of 3? No, it is not. When skip counting by 3, 17 is not a number said. Likewise, there is no factor that can be multiplied by 3 to equal 17.
Facts of Factor Pairs
- Every number has 1 as one of its factors.
- If a number's only factors are 1 and the number itself, the number is prime.
- If a number has more factors than 1 and itself, the number is composite.
- Zero is not a factor of any other number besides itself because multiplying a number by 0 will always result in 0. So, the factors of 0 are infinite!
- In a division equation, the divisor and quotient are factors of the dividend if the remainder is 0.
 |
What are Factor Pairs of 12, 13, 2?
- Factor pairs of 12
- 1 and 12, 2 and 6, 3 and 4
12 is a composite number because it has more factors than 1 and itself.
- Factor pair of 13
- 1 and 13
13 is a prime number because its only factors are 1 and itself.
- Factor pair of 2
- 1 and 2
2 is also a prime number because its only factors are 1 and itself.
Lesson Summary
Factors are numbers multiplied by each other to equal a product. Any numbers can be factor pairs if they are being multiplied. One way factors can be found is by counting the rows and columns in an array.
Factors can also be found through divisibility. If a number can be divided by another without any remainder, that number is a factor. Every number has 1 as a factor. Some numbers only have 1 factor pair including 1 and itself. Those numbers are prime. Other numbers have more than 1 factor pair and are called composite numbers. Multiples are the answers to multiplication problems and can also be found by skip-counting by a number.
Pairing Up
Factor pairs are pairs of factors we multiply together to get a certain product. Let's go back to our second multiplication sentence: 3 * 4 = 12.
4 and 3 is one factor pair that can give us a product of 12. But we can also write the following multiplication sentences that give a product of 12:
- 1 * 12 = 12
- 2 * 6 = 12
So, the factor pairs that will give us a product of 12 are 1 and 12, 2 and 6, and 3 and 4.
Generally speaking, the larger a number is, the more factor pairs it will have. This isn't true for prime numbers because their only factor pairs are 1 and the number itself. For example, 937 is a large number, but it's also a prime number. So, its only factor pair is 1 and 937.
Examples
Let's determine the factor pairs for 40. We can write the following multiplication sentences to get a product of 40:
- 1 * 40 = 40
- 2 * 20 = 40
- 4 * 10 = 40
- 5 * 8 = 40
So, 40's factor pairs are 1 and 40; 2 and 20; 4 and 10; 5 and 8.
Up for a challenge? Let's try a 3-digit number. We'll find the factor pairs for 100:
- 1 * 100 = 100
- 2 * 50 = 100
- 4 * 25 = 100
- 5 * 20 = 100
- 10 * 10 = 100
100's factor pairs are 1 and 100; 2 and 50; 4 and 25; 5 and 20; 10 and 10.
Zero - A Special Case
What about 0? Let's look at the multiplication sequences that give us a product of 0:
- 0 * 1 = 0
- 0 * 2 = 0
- 0 * 3 = 0
- 0 * 4 = 0
- 0 * 1,000,000 = 0
You get the picture. 0 has an infinite number of factor pairs because any number times 0 equals 0!
Lesson Summary
In multiplication, the numbers we multiply together are factors. The answer we get when we multiply is the product. Two numbers that we can multiply together to get a certain product make a factor pair.
Factor Pair Overview
 |
| Terms | Explanations |
|---|---|
| Factors | the numbers you multiply together |
| Product | the answer we get when we multiply two factors together |
| Factor pairs | pairs of factors we multiply together to get a certain product |
Learning Outcomes
When this lesson is over, you should be able to:
- Define factors
- Describe a product
- Explain what makes up a factor pair
To unlock this lesson you must be a Study.com Member.
Create your account
Video Transcript
Definition of a Factor Pair
Let's say a mother in your neighborhood hires you to babysit for $75 a night, and you can babysit four nights of the week. Of course, to figure out your weekly income, we would multiply the nightly income by the number of nights you can work:
75 * 4 = 300
You'll make $300 in one week! Not bad.
Factors are the numbers you multiply together. In this multiplication sentence, 75 and 4 are the factors. 300 is the product, which is the answer we get when we multiply two factors together.
So, in this multiplication sequence, 3 * 4 = 12, 3 and 4 are the factors, and 12 is the product.
Pairing Up
Factor pairs are pairs of factors we multiply together to get a certain product. Let's go back to our second multiplication sentence: 3 * 4 = 12.
4 and 3 is one factor pair that can give us a product of 12. But we can also write the following multiplication sentences that give a product of 12:
- 1 * 12 = 12
- 2 * 6 = 12
So, the factor pairs that will give us a product of 12 are 1 and 12, 2 and 6, and 3 and 4.
Generally speaking, the larger a number is, the more factor pairs it will have. This isn't true for prime numbers because their only factor pairs are 1 and the number itself. For example, 937 is a large number, but it's also a prime number. So, its only factor pair is 1 and 937.
Examples
Let's determine the factor pairs for 40. We can write the following multiplication sentences to get a product of 40:
- 1 * 40 = 40
- 2 * 20 = 40
- 4 * 10 = 40
- 5 * 8 = 40
So, 40's factor pairs are 1 and 40; 2 and 20; 4 and 10; 5 and 8.
Up for a challenge? Let's try a 3-digit number. We'll find the factor pairs for 100:
- 1 * 100 = 100
- 2 * 50 = 100
- 4 * 25 = 100
- 5 * 20 = 100
- 10 * 10 = 100
100's factor pairs are 1 and 100; 2 and 50; 4 and 25; 5 and 20; 10 and 10.
Zero - A Special Case
What about 0? Let's look at the multiplication sequences that give us a product of 0:
- 0 * 1 = 0
- 0 * 2 = 0
- 0 * 3 = 0
- 0 * 4 = 0
- 0 * 1,000,000 = 0
You get the picture. 0 has an infinite number of factor pairs because any number times 0 equals 0!
Lesson Summary
In multiplication, the numbers we multiply together are factors. The answer we get when we multiply is the product. Two numbers that we can multiply together to get a certain product make a factor pair.
Factor Pair Overview
|
| Terms | Explanations |
|---|---|
| Factors | the numbers you multiply together |
| Product | the answer we get when we multiply two factors together |
| Factor pairs | pairs of factors we multiply together to get a certain product |
Learning Outcomes
When this lesson is over, you should be able to:
- Define factors
- Describe a product
- Explain what makes up a factor pair
To unlock this lesson you must be a Study.com Member.
Create your account
Frequently Asked Questions
What are factor pairs of 24?
There are several factors of 24. The factor pairs are 1 and 24, 2 and 12, 3 and 4, and 4 and 6.
What are the factor pairs of 12?
The factor pairs of 12 are 1 and 12, 2 and 6, and 3 and 4. 12 can be divided by any of these factors without a remainder.
What is a factor pair for 2?
2 has only one factor pair- 1 and 2. Since 2 has no other factor pairs, it is a prime number.
What are factors and factor pairs?
Factors are numbers that are multiplied together to equal a product. Factor pairs are the two numbers that are multiplied.
How do you find the factor pairs?
You can find factor pairs by creating an array for the total. The number of rows and columns are a factor pair. You can also use division to find factor pairs. When a number is divided by another, the divisor and quotient are factors, as long as the remainder is 0.
Register to view this lesson
Are you a student or a teacher?
Unlock Your Education
See for yourself why 30 million people use Study.com
Become a Study.com member and start learning now.
Become a MemberAlready a member? Log In
BackResources created by teachers for teachers
Over 30,000 video lessons
& teaching resources‐all
in one place.
I would definitely recommend Study.com to my colleagues. It’s like a teacher waved a magic wand and did the work for me. I feel like it’s a lifeline.
Jennifer B.
Teacher
Back
Factor Pairs | Product & Examples
Related Study Materials
Explore our library of over 84,000 lessons
Browse by subject