# Factor and multiples worksheets: Factors and Multiples Worksheet

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## 50+ Factors and Multiples worksheets on Quizizz

Math Factors and Multiples: Discover a vast collection of free printable worksheets to help students master the essential concepts of factors and multiples, enhancing their mathematical skills.

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### Subjects

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Algebra Addition Subtraction Percents, Ratios, and Rates Geometry Number Sense Numbers 0-10 Numbers 11-20 Two-Digit Numbers Number Patterns Number Theory Prime and Composite Numbers Greatest Common Factor Factors and Multiples Least Common Multiple Scientific Notation Three-Digit Numbers Multi-Digit Numbers Exponents Integers and Rational Numbers Irrational Numbers Multiplication Division Mixed Operations Fractions Decimals Measurement Money Math Data and Graphing Math Word Problems Math Puzzles The Basics Expressions and Equations Linear Functions Factoring Inequalities and System of Equations Monomials Operations Quadratic Polynomial Operations Radical Expressions Rational Expressions Statistics and Probabilities Fundamentals and Building Blocks Equations and Inequalities System of Equations and Quadratic Complex Numbers Matrices Functions Operations Logarithms Conic Sections Trigonometric Functions Sequences and Series Algebra 2 Graphs & Functions Probability & Combinatorics Trigonometry arithmetic and number theory calculus probability and statistics

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### Explore printable Factors and Multiples worksheets

Factors and Multiples worksheets are essential tools for teachers looking to enhance their students’ understanding of number sense and number theory in math. These worksheets provide a variety of engaging and challenging exercises that help students grasp the concepts of factors, multiples, prime numbers, and divisibility rules. By incorporating these worksheets into their lesson plans, teachers can create a comprehensive and interactive learning experience for their students. With a wide range of difficulty levels, these worksheets cater to the diverse needs of students in different grades, ensuring that each learner can progress at their own pace. Factors and Multiples worksheets are an invaluable resource for educators who want to foster a strong foundation in math and number sense among their students.

Quizizz offers a unique platform that combines the benefits of Factors and Multiples worksheets with interactive quizzes and other engaging learning resources. Teachers can create customized quizzes that align with their lesson plans, enabling them to assess their students’ understanding of number sense and number theory concepts effectively. In addition to quizzes, Quizizz also provides a vast library of educational resources, including worksheets, games, and presentations, which can be easily integrated into the classroom. This comprehensive approach to learning ensures that students remain engaged and motivated, ultimately leading to better retention and mastery of math concepts. By incorporating Quizizz into their teaching strategies, educators can create a dynamic and interactive learning environment that fosters a deep understanding of Factors and Multiples, as well as other essential math topics.

## Factors and Multiples: The Factor Factory Activity

 Listen to this Lesson:

Factors and Multiples

When I taught fifth grade, my school had a meeting with incoming fourth graders and their parents.  Some of the most asked questions had to do with math and multiplication facts.  I remember telling them that it’s not just knowing your times tables, what’s more important is being able to recognize factors and multiples of numbers – to be able to look at a number and know what can divide into it.   Factoring is a skill that students use in fractions and division, but also problem solving, algebra and even quadratic equations when they move through more advanced math in middle school.

How to Introduce Factors and Multiples

I like to introduce factors as building blocks.  Have you ever seen the LEGO Movie?  I have used scenes from the movie to talk about factors.  If you are a “Master Builder” then you can see the blocks that fit together to build the number.  Factors are the blocks that multiply together to create the product.

I like to tell my students that if they work to become a Master Builder, they will “see” the factors of any number.  I also like to talk about the Factor Factory.  Factors are equal to or less than the number and they multiply together to make the product.  Just like a factory- Factors make products.

Students Often Confuse Factors and Multiples

Factors (factories) make products.   And Multiples Make More, they multiply.  There are an infinite amount of multiples, but a finite number of factors.

I like to play scenes from the LEGO movie, especially where the main character realizes he is a Master Builder. You can find the movie or links to these scenes.  When students successfully find all the factors, we also celebrate by rocking out to Everything is Awesome (I usually just use the first 48 seconds of the song).

Set up for the Factors and Multiples Activity

• Bring in LEGOS, duplos, blocks or unifix/snap cubes
• Index cards or small pieces of paper
• Coins or tokens
• Graph paper
• Playing cards
• Hundreds Chart
• Factors and Multiples Worksheet for every student
• Video clip or lego instructions book

Put students in small groups or create stations around the room with the following materials:

Station 1: Playing Cards, Graph paper

Station 2 : Dice and Playing cards, coins/tokens

Station 3: Coin, hundred chart, index cards

Station 4: Dice and Legos/blocks

Launch the Factor Factory Activity

You can find a clip from The LEGO Movie to help you talk about what it means to be a “Master Builder”.   Being a Master Builder is not just following the instructions, but “seeing” the pieces or parts that you need to build the product, as shown in the image below.

A goal of knowing the factors or factoring a number is seeing ALL of the factors that can be used to create that number.  A Master Builder will “see” them all.  A good way to show how to gather all of the factors is to build up the number with factor pairs.

I like to talk about “closing it up, or wrapping up the product”.

So a good way to show this is to tell the students to write the number they want to factor on the top.  That’s the goal.  That’s the product they’re building.  Can they see all of the factors, like a “Master Builder” can see the correct blocks?

The Universal Factor

The best way to find all of the factors is to start with the universal factor – 1.   1 is a factor for every number.  A great way to show this is to have 6 coins or cards.   Ask students to put them into equal rows.  1 row of 6, 2 rows of 3, 3 rows of 2 and 6 rows of 1.  Talk about how the factors are the arrays or arrangements that they can make with equal rows.    With any number, you can always have 1 row of something.  1 is always a factor.

Help the students see the factor pairs by using their cards or coins, but also show them how they can factor by knowing their multiplication facts.

Show the students how to write the number they are factoring, on the top of that “factory”  and underline it, like this:

Then, inside the factory, write the factor pairs.  Always start with 1 x it’s factor pair.  Then try 2 and write its pair, then 3, then 4, then 5, then 6!  If they build all the way to the factory number then they will find all of the factors.

Students can also show these pairs in arrays with their coins or cards.

Similar to image below:

Ask the students if they notice any similarities between the arrays and their factories?

A 2×3 array is basically the same as a 3×2 array.   So show how in the factory, as soon as a pair is repeated, the factory can be “closed” or wrapped up.  When they write the factors as pairs, the students can find all of the factors faster.  Do they need to count all the way to 6?  No.  They can find all of the factor pairs 1,6,2,3 by the time they get to 3, because that pair gets repeated.

The Difference Between Factors and Multiples

This activity is to practice finding all of the factors.  But before we begin, I like to talk about the difference between factors and multiples.  One way I do that is either call on a volunteer or ask the class to stand up and say the multiples of 6 out loud.  I stand there, I even help them out if they need it, and I wait.  I wait longer than you would think.  I let them keep going, and going, and going.  (If you really want to make a point, you could do a smaller number like multiples of 2 or 3, but I like to use 6 to show that it has several factors, but the multiplies never end).   The point is to show that multiples make more, they get bigger, and there is no end.  But factors, even though they involve multiplication, have a set amount that can make up the number.  Once you have the class list multiples of 6 and find the factors of 6, they can see the difference between the two terms.

Check their understanding by trying to factor 15.

Use the Factory as well as cards or tokens/coins to find all of the factors together.

Remind the students that as soon as a pair is repeated, they have found them all.  They are Master Builders when they’ve found all of the factors!

The Factor Factory uses the idea of building up from 1 and finding the factor pair.  This is a great way to help students work on their times tables while strategically becoming a master builder of math.  Once they have found the factors, they can prove it with arrays of cards/coins.  There are only 4 ways to show 15:  1×15 or 15×1  and 3×5 or 5×3.  2 pairs.

In the activity, the students must use a number (or product) and build it with its factor pairs.  They must find all of the factors and become the Master Builder.  Students can show all of the arrays as well as write out the factors in the Factor Factory.

The Factor Factory Activity

A good way to practice factors is to make stations and provide lots of practice.  Stations can help students find numbers, show or color arrays, and create factor factories, all of which will help them increase their fluency with finding factors.

Here is a list of stations that can help you get the students moving, generate numbers and find factors.

Station 1 :  Playing Cards:  Draw 2-3 cards, multiply the face value together and then find ALL factors of that product.

Show arrays on graph paper.

Station 2:  Roll a dice and draw a card.  Find the product.  Then find ALL of the factors of that product.

Show arrays with coins or tokens.

Station 3:  Flip a coin onto a Hundreds Chart or close your eyes and randomly choose a number.  Find the factors of the number you land on.  Make a factor factory with index cards showing the factors.

Station 4:  Roll 2 dice – if you roll a 1, roll again. Find the product.  Build arrays with lego blocks or blocks.  Each brick can be 1.  For example:  8 could be built with 8 blocks, but 2 rows of 4 or 4 rows of 2 or 1 row of 8 etc…

Reflecting on the Factor Activity

Use these questions to guide a discussion with students (Note: Written reflection questions are also included at the end of the Factors and Multiples Worksheet):

• Which number that you found has the most factors? The least?
• How did the arrays help show the factors? Explain.
• We know that every number has a factor of 1 and itself. What do you know about factors of even numbers?
• Can you find ALL of the factors of 30? List them.
• Can you find ALL of the multiples of 30?

Factors and Multiples Extensions

• Students can Make a Factor City for a certain number. – For example 100. On graph paper or with blocks, create buildings that each have 100 blocks/squares.  However, each building has a different shape because they are built in factor pair arrays. Using lego bricks or blocks, students can make it 3D.
• Draw a sign or poster that advertises certain “Factories.”  Draw and color some factories with all of the factors inside for each one.  Be sure to choose numbers that are higher than 24.

FREE Factors and Multiples Worksheets and Resources

These are all PDF Files. They will open and print easily. The Student Edition Files are labeled SE and the Teacher Editions Files are labeled TE. Click the links below to download the different resources.

• 4-3 Assignment SE – Factors and Multiples (PDF)
• 4-3 Assignment TE – Factors and Multiples (Member Only)
• 4-3 Bell Work SE – Factors and Multiples (PDF)
• 4-3 Bell Work TE – Factors and Multiples (Member Only)
• 4-3 Exit Quiz SE – Factors and Multiples (PDF)
• 4-3 Exit Quiz TE – Factors and Multiples (Member Only)
• 4-3 Guided Notes SE – Factors and Multiples (PDF)
• 4-3 Guided Notes TE – Factors and Multiples (Member Only)
• 4-3 Interactive Notebook – Factors and Multiples (PDF)
• 4-3 Lesson Plan – Factors and Multiples (PDF)
• 4-3 Online Activities – Factors and Multiples (PDF)
• 4-3 Slideshow – Factors and Multiples (PDF)

Factors and Multiples Worksheets and Resources

To get the Editable versions of these files Join us inside the Math Teacher Coach Community! This is where we keep our full curriculum of 4th Grade Math Lessons and Activities.

• 4-3 Assignment SE – Factors and Multiples  (Member Only)
• 4-3 Assignment TE – Factors and Multiples (Member Only)
• 4-3 Bell Work SE – Factors and Multiples (Member Only)
• 4-3 Bell Work TE – Factors and Multiples (Member Only)
• 4-3 Exit Quiz SE – Factors and Multiples (Member Only)
• 4-3 Exit Quiz TE – Factors and Multiples (Member Only)
• 4-3 Guided Notes SE – Factors and Multiples (Member Only)
• 4-3 Guided Notes TE – Factors and Multiples (Member Only)
• 4-3 Interactive Notebook – Factors and Multiples (Member Only)
• 4-3 Lesson Plan – Factors and Multiples (Member Only)
• 4-3 Online Activities – Factors and Multiples (Member Only)
• 4-3 Slideshow – Factors and Multiples (Member Only)

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Don’t Forget to Pin The Factor Factory Activity…

This lesson is from…

Unit 4 – Multi-Digit Whole Number Division

• 4-1  Division Using Area Models
• 4-2  Whole Number Quotients and Remainders
• 4-3  Factors and Multiples
• 4-4  Prime and Composite Numbers
• 4-5  Division of Multiples of 10, 100, and 1,000 by Single-Digit Numbers
• 4-6  Three and Four-Digit Division with Divisors of 2, 3, 4, and 5
• 4-7  Division with a Zero in the Dividend or in the Quotient
• 4-8  Division with Divisors of 6, 7, 8, and 9
• 4-9  Solve One-Step Division Word Problems

## Divisors and multiples. Factorization.

Divisors and multiples. Factoring .

5th class

Fgos

Goals:

Educational:

Learn what is called a divisor and a multiple; repeat prime and composite numbers; to acquaint with decomposition into prime factors; repeat the power of a number; find divisors and multiples of numbers; it is correct to use terms in speech: divisor, multiple, prime number, composite number.

Educational:

Education of responsibility, accuracy, discipline, culture of communication.

Developing:

To develop the ability to highlight the main thing, to generalize the studied facts.

Repetition:

Write the product as a power: 0 6 6 6 =

5⁴

5∙5∙5∙5=

2 2 2 2 2 2

x⁴

x ∙ x ∙ x ∙ x =

Learning new material.

Factor the number 60 in all possible ways:

60 = 2 30 = 3 20 = 4 15 = 5 12 = 6 ∙ 10

b) by 3 factors:

10 = 2 ∙ 2 ∙ 15 = 3 ∙ 4 ∙ 5

c) by 4 multipliers:

60 = 2 2 3 5

60 = 2 2 3 5 9 0021

prime factors

The number 280 is the product of the numbers 28 and 10.

10

28

.

.

2

5

2 ∙2 900 07

7

280=2 ∙2 ∙2 ∙3∙5∙7= ∙ 3 ∙ 5 ∙ 7

Let’s remember what is called the divisor of the number huh?

Divisor of natural number a is the natural number by which a is divisible without a remainder.

For example , the number 28 0021 :

1, 2, 4, 7, 14, 28

(28:1=28, 28:2=14, 28:4=7, 28:7=4, 28:14=2, 28:28=1)

Divisor of

1, 2, 4, 8.16

Find all divisors numbers 45 :

1, 3, 5, 9, 15, 45

Find all divisors of 17 :

Let’s do #596(1 column)

Physical education minute

• Choose the divisor of the number 15: 7, 9, 5. Raise your hands up so many times.
• Select the multiples of 4: 7, 8, 10. Turn your heads left and right as many times.
• Choose a prime number from the data: 4, 5, 8. Do this many tilts left and right.
• Choose a compound from the given numbers: 5, 7, 6. Perform as many squats.

Divisor of

Divisor of any natural number 1

Multiple of a

Multiple of natural number a 9 0005 is a natural number that is divisible without remainder by and .

For example, the first five multiples of 5 5, 10, 15, 20, 25

DISCLAIMER : If the natural number a is evenly divisible by the natural number b , the number a is called multiples of b b divisor numbers a

• 1, 2, 4, 5, 8, 10, 20, 40 are divisors

06 number 40.

• And number 40

multiples of of each of these numbers

Write down all divisors of 6: 1; 2; 3; 6

Write down all multiples of 6:

6; 12; 18; 24; 30 etc.

(all cannot be listed)

The smallest divisor of any natural number a is the number 1, and the largest divisor is the number itself a

04 number k then and the sum a + b is also divisible by the number k

• is divisible by 4
• is divisible by 4 21

2. If neither the number a nor the number b are divisible by the number k , then their sum a + b may or may not be divisible by the number k

9 is not divisible 5, 7 is not divisible by 5

(9 + 7) is not divisible by 5

4 is not divisible by 3, 8 is not divisible by 3

(4 + 8) is divisible by 3

No. 601.604

Divisors and multiples

Task 1.

) numbers 17

Answers to task 1.

a) 1, 2, 4, 5, 10, 20

b) 1, 17

Divisors and multiples

Task 3.

Write down the number that is: 0020 a) a divisor of 20 and 30, b) a multiple of 4 and 6

Answers to the task 3.

a) 1, 2, 5, 10

b) 12, 24, 36 …

Divisors and multiples

Assignment for independent work. Write down all divisors of 28 and three multiples of 28.

Answers to the task:

a) divisors of 28: 1, 2, 4, 7, 14, 28 90 006

b) multiples 28: 28, 56, 84, 112, 140,…

OPTIONAL (if time permits) Divisors and multiples of

Which of the numbers 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 18, 30

• are divisors of 24
• are multiples 6
• are divisors of 20 and 24
• are divisors of 24 and multiples of 4

9 0002

Homework:

• No.

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