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Greatest Common Factor (GCF) Worksheets

A large collection of GCF worksheets is meticulously drafted for students in grade 5 through grade 8. GCF is also known as 'greatest common divisor'(GCD), 'highest common factor'(HCF), 'greatest common measure'(GCM) or 'highest common divisor'(HCD). Download and print these GCF worksheets to find the GCF of two numbers, three numbers and more. Try some of these handouts for free!

GCF: Descriptive

List the factors for each pair of numbers. Then, compare to determine the GCF of the two numbers. The printable worksheets are categorized into three levels based on the range of numbers.

• Download the set

GCF of Two Numbers: Standard

Use the prime factorization method to find the GCF for each pair of numbers. This batch of multi-level worksheet pdfs contains a total of 150 problems for 5th grade and 6th grade students. Use the answer key to validate your solutions.

GCF of Two Numbers using Venn Diagrams | Easy

Write down the factors for each pair of numbers in the Venn diagram. Then, list out the common factors in the intersection. The largest factor listed in the overlapping region is the GCF. This set includes numbers up to 25.

GCF of Two Numbers using Venn Diagrams | Moderate

Brighten your math class by using Venn Diagrams to find the GCF of two numbers. Featuring numbers up to 99, this compilation requires learners to list out the factors, place the common factors in the overlapping region, and find the GCF.

GCF and Distributive Property

Being good at something isn’t enough, aim for greatness! Choose our pdf worksheets on GCF and Distributive Property and practice rewriting expressions as the product of the GCF and a sum using the property.

Simplify Fractions using GCF | Easy

Find the GCF for the numerator and the denominator of the given fraction in this set of printable worksheets. Then, reduce the fraction to its lowest term by dividing the numerator and denominator by the GCF. Numbers up to 25 are included in this section.

Simplify Fractions using GCF | Moderate

Facilitate better understanding of GCF by reviewing your skill with this bundle of printable worksheets that features numbers up to 99. Practice finding the GCF and simplifying the fraction using the GCF.

GCF, LCM and the Product

There’s a solid relationship between GCF, LCM, and the product of two numbers. Broaden your knowledge with our pdf worksheets and be the first in class to ace this enthralling topic!

GCF of Three Numbers | Easy

In this bunch of 7th grade and 8th grade pdf worksheets, determine the GCF for the set of three numbers. Apply prime factorization method to list out the common factors. Multiply the common factors to obtain the GCF of the three numbers.

GCF of Three Numbers | Moderate

It’s time to get acquainted with GCF of three numbers by working out the exercises in these pdfs covering numbers up to 99. Work out the GCF by finding the product of the prime factors common to all three numbers.

GCF and LCM word problems

Let’s explore GCF and LCM in the real word using heaps of realistic word problems! Solve life-like situations that impel you to think about the applications of great common factor and least common multiple like never before!

GCF of Polynomials

Gain an in-depth knowledge in finding the Greatest Common Factor of polynomials with these high school worksheets available in easy and moderate levels, find the GCF of two or three monomials, GCF of polynomials, find the GCF using the division method and more!

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5th Grade Factors and Multiples Worksheets

In 5th Grade Factors and Multiples Worksheets we will find the multiples of a given number, find the prime factors of a number, HCF of co-prime number, LCM of two co-prime numbers, HCF of two co-prime numbers, common multiples of three numbers, word problems on LCM and word problems on HCF.

I. Write the first three multiples of the given numbers.

II. Find the prime factor of 84.

III. Find the number:

(i) A multiple of 7 which lies between 30 and 40.

(ii) A multiple of 5 and 2 which is 2 more than the third multiple of 6.

(iii) A multiple of 3 and 5 greater than 42 but less than 47.

(iv) 2 digit prime number less than 47. The product of my digits is 21.

(v) Multiple of 3 but not of 6 and 9 greater than 22 but less than 37.

(vi) Two digit odd composite number. Sum of my digits is 12 and I am greater than 89.

IV. Fill in the blanks:

(i) 3 × 5 = 15. Here 3 and 5 are …………… of 15.

(ii) 6 × 7 = 42. Here 42 is the …………… of 6 and 7.

(iii) The numbers with only 2 factors are called …………… numbers.

(iv) The HCF of co-prime number is ……………

(v) A number can have …………… multiples.

(vi) LCM of two co-prime numbers is their ……………

(vii) HCF of two or more numbers always …………… their LCM.

V. Find the HCF of the given numbers.

(i) 15 and 20

(ii) 24, 36 and 42

(iii) 36 and 170

(iv) 90, 108 and 126

VI.  Write the prime numbers between 11- 30.

VII.  Find the common multiples of 2, 8 and 12.

VIII.  Check the divisibility of given numbers.

(i) 86, 190 by 3

(ii) 47, 815 by 3

(iii) 2, 37, 405 by 11

(iv) 81, 620 by 4

IX.  Find the LCM of the given numbers.

(i) 42 and 84

(ii) 55 and 105

(iii) 32 and 124

(iv) 35, 25 and 15

(v) 80, 140 and 200

X.  Multiple Choice Questions (MCQ) on Factors and Multiples:

     Tick ( ✔ )  the correct option.

(i) The HCF of 276, 336 and 420 is

(ii) The LCM of 18, 24, 36 and 42 is (a) 182

(iii) The LCM of 72, 96 and 104 is

XI. State True or False.

(i) The largest 7-digit number divisible by 9 is 9999999.

(ii) Difference of two even numbers is odd.

(iii) Numbers divisible by 2 are called even numbers.

(iv) The H.C.F. of two consecutive odd numbers is 1.

XII. Fill in The Blanks:

(i) The H.C.F. of 20 and 27 is _____ .

(ii) The H.C.F. of two numbers always _____ their LCM.

(iii) The greatest 2-digit prime number is _____.

(iv) Every multiple of 2 is an _____ number.

(v) The prime factors of 135 are _____.

XIII.  Find the HCF of the following:

(a) 144, 180 and 192

(b) 136, 170 and 255

(c) 161 and 345

(d) 513, 621 and 783

(e) 289, 391 and 884

XIV. Word Problems on Factors and Multiples:

(i) Find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3 respectively.

(ii) A room is 7 m 35 cm broad and 11 m 55 cm long. The floor of the room is to be covered with square tiles. Find the length of the largest tile that can be used.

(iii) Determine the longest tape which can be used to measure exactly the lengths 2 m 76 cm, 12 m 42 cm and I m 38 cm.

(iv) In a seminar, the number of participants in Hindi, English and Mathematics are 106, 159 and 265 respectively. Find the minimum number of rooms required, if in each room the same number of participants is to be seated and all of them are for the same subject.

(v) Find the smallest number which when divided by 21, 28, 36 and 45 leaves a remainder 9 in each case.

(vi) Find the smallest number which when added to 9 is exactly divisible by 12, 15, 20 and 27.

(vii) What is the least number that must be subtracted from 3000 so that the difference is exactly divisible by 32, 36 and 48?

(viii) Find the least 4-digit number which when divided by 24, 16 and 12 leaves a remainder 5

(ix) The LCM of 285 and 63 is 252 . Find their HCF.

(x) The LCM of two numbers is 1344 and their HCF is 4. If one of the numbers is 84, find the other number.

(xi) Nairitee visits the library every fourth day and Nitheeya every sixth day. Find out days on which both meet in the library in the month of December. 

Answers on 5th Grade Factors and Multiples Worksheets are given below to check the exact answers of the questions. 

I.  (i) 4, 8 , 12

(ii) 7, 14, 21

(iii) 13, 26, 39

II.  2 × 2 × 3 × 7

III.  (i) 35

IV.  (i) factors

(ii) multiple

(iii) prime

(vi) product

(vii) divides

V.  (i) 5

VI.  13, 17, 19, 23, 29

VII.  24

VIII.  (i) divisible

(ii) divisible

(iii) not divisible

(iv) divisible

IX.  (i) 84

X.   (i) The HCF of 276, 336 and 420 is  (a) 12

(ii) The LCM of 18, 24, 36 and 42 is  (b) 504

(iii) The LCM of 72, 96 and 104 is  (c) 3744

XI.  (i) True

XII.  (i) The H.C.F. of 20 and 27 is 1.

(ii) The H.C.F. of two numbers always a factor their LCM.

(iii) The greatest 2-digit prime number is 97.

(iv) Every multiple of 2 is an even number.

(v) The prime factors of 135 are 3 and 5.

XIII.  (a) HCF of 144, 180 and 192 is 12

(b) HCF of  136, 170 and 255 is 17

(c) HCF of  161 and 345 is 23

(d) HCF of  513, 621 and 783 is 27

(e) HCF of  289, 391 and 884 is 17

(ii) 105 cm

(iii) 138 cm

(viii) 1013

(xi) 12 th  day and 24 th  day

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A collection of math worksheets on finding factors, greatest common factors, and factor trees, as well as prime numbers & composite numbers.

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Prime Factorization Worksheets

Welcome to our Prime Factorization Worksheets page.

Here you will find our selection of worksheets involving finding prime factorizations for a range of numbers, and for solving prime factor problems.

We have a range of sheets at different levels of difficulty.

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Using these factor tree worksheets will help your child to:

• practice prime factorization of a range of numbers;
• solve problems involving prime factorization;
• use and understand exponential notation.

These sheets are aimed at students from 6th grade and upwards.

We also have a link to our Prime Factorization Calculator which will quickly and easily show you all the prime factors of any number.

There is also a quick quiz at the bottom of the page where you can test your skill at prime factorization and get immediate feedback!

What is prime factorization?

To find out more about prime factorization, including how it works and to look at some worked examples, take a look at our prime factorization support page.

• What is Prime Factorization support page

Examples of Prime Factorization

Example 1) Find the prime factorization of 40.

40 is even, so we know that 2 is a factor (as well as being prime)

40 = 2 x 20.

Now we move on to the number 20.

Again 20 is even, so 2 is a factor.

20 = 2 x 10

So 40 = 2 x 20 = 2 x 2 x 10

Now we factorize 10 into 2 x 5 (both prime numbers) and we cannot go any further, as all the numbers are prime.

So 40 = 2 x 20 = 2 x 2 x 10 = 2 x 2 x 2 x 5

Our final answer is 40 = 2 x 2 x 2 x 5 = 2 3 x 5

Example 2) Find the prime factorization of 45.

45 is odd, so 2 is not a factor.

As the number ends in a 5 we know that 5 is a factor.

45 = 5 x 9.

Now we have to factorize 9.

9 = 3 x 3 (which is a prime number).

This gives us:

45 = 5 x 9 = 5 x 3 x 3

Our final answer is 45 = 3 x 3 x 5 = 3 2 x 5

Example 3) Find the prime factorization of 126.

126 is even, so 2 is a factor.

126 = 2 x 63

Now we need to factorize 63.

63 = 7 x 9.

7 is prime, but 9 is not

126 = 2 x 63 = 2 x 7 x 9 = 2 x 7 x 3 x 3

Our final answer is 126 = 2 x 3 x 3 x 7 = 2 x 3 2 x 7

All the worksheets have answers provided. The answers are given with the factors in ascending order.

The sheets get gradually harder in each section.

We have split the sheets into 3 different sections:

• Our first section involves straightforward prime factorization of different numbers.
• Our next group of sheets involves solving prime factorization riddles.
• Our final group of sheets involves finding all possibilities in our prime factorization challenges.

Prime Factorization Worksheets - 1st Section

• The two sheets just has straightforward prime factorization of a range of numbers.
• The third sheet is harder, and involves using exponential notation and looking at prime factorization from different starting points
• Prime Factorization Sheet 1
• PDF version
• Prime Factorization Sheet 2
• Prime Factorization Sheet 3

Prime Factorization Worksheets - Riddles - 2nd Section

These sheets involve solving prime factorization riddles.

There are 2 riddles on each sheet and 8 possible answers.

By correctly working out the clues in each riddle, all the incorrect answers are eliminated leaving just one correct answer.

• Prime Factorization Riddles Sheet 1
• Prime Factorization Riddles Sheet 2

Prime Factorization Worksheets - Challenges - 3rd Section

Our prime factorization challenges are a great way to stretch more able students.

The challenges involve finding all possible numbers that have certain features involving prime factors.

• Prime Factorization Challenges 1
• Prime Factorization Challenges 2

Prime Factorization Walkthrough Video

This short video walkthrough shows several problems from our Prime Factorization Worksheet 3 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on this page, check out the video!

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

• Factors and Multiples Worksheets

We have worksheets to help you understand more about factors and multiples.

They are aimed at a 4th/5th grade level.

• Prime Factorization Calculator

Our prime factorization calculator will help you factor any number into a product of its prime factors.

It will show the answer in exponential form as well as standard form.

You can use this calculator to check that your prime factors in your factor trees are correct.

• Factor Tree Worksheets

Using factor trees is a great visual way to understand prime factorization.

The worksheets on the link below are at an easier level to the sheets on this page and help children learn all about factor trees and prime factors.

• Greatest Common Factor Worksheets

As well as our calculator, we also have a range of greatest common factor worksheets.

These sheets have been designed for 6th and 7th grade students.

They will help students learn and practice finding the greatest common factor of numbers up to 100.

• Least Common Multiple Worksheets

We have a range of worksheets on how to find the least common multiple of two or three numbers.

The sheets vary in difficulty, and are suitable for 6th grade and up.

Sieve of Erastosthenes

The Sieve of Erastosthenes is a method for finding what is a prime numbers between 2 and any given number.

Eratosthenes was a Greek mathematician (as well as being a poet, an astronomer and musician) who lived from about 276BC to 194BC.

If you want to find out more about his sieve for finding primes, and print out some Sieve of Eratosthenes worksheets, use the link below.

• Sieve of Eratosthenes page

Want to find out more about primes?

Take a look at our Prime Number page which clearly describes what a prime numbers is and what they are not.

There are also many different questions about prime numbers answered, as well as information about the density of primes.

• What is a Prime Number

Divisibility Rules 1-10 Chart

We have a range of charts which can help you determine whether a number between 1 and 10 is a factor of a number.

• Divisibility Rules 1-10 Charts

6th Grade Mental Math Quizzes

Here you will find a range of printable mental math 6th grade quizzes for your child to enjoy.

Each worksheet tests the children on a range of math topics from number facts and mental arithmetic to geometry, fraction and measures questions.

A great way to revise topics, or use as a weekly math quiz!

• Mental Math Worksheets 6th Grade

Prime Factorization Online Quiz

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This quick quiz tests your knowledge of prime factorization with numbers up to 120.

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Common Factors Study Guide

What are common factors.

Common factors are numbers that divide two or more numbers evenly. In other words, they are the numbers that are factors of two or more given numbers .

Finding Common Factors

To find the common factors of two or more numbers , you can list all the factors of each number and then find the numbers that appear in the factor lists of all the given numbers .

Find the common factors of 12 and 18.

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

Common factors: 1, 2, 3, 6

Using Multiplication to Check

To check if a number is a common factor of two given numbers , you can multiply the number by another factor to see if it equals one of the given numbers . If it does, then it is a common factor.

Is 3 a common factor of 12 and 18?

1. Memorize the multiplication table to quickly identify common factors.

2. Practice finding common factors of different numbers to strengthen your skills.

3. Use the multiplication method to check if a number is a common factor.

Read More...

◂ Math Worksheets and Study Guides Fifth Grade. Common Factors

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Factoring Trinomials Worksheets (a = 1)

Related Topics: More Math Worksheets More Grade 7 Math Lessons Grade 7 Math Worksheets

There are three sets of factoring trinomials worksheets:

• Factoring Trinomials (a = 1)
• Factoring Trinomials (a > 1)
• Factor Perfect Square Trinomials

Examples, solutions, videos, and worksheets to help Grade 6 and Grade 7 students learn how to factor trinomials, ax 2 + bx + c for a = 1.

How to factor trinomials?

There are five sets of factoring trinomials worksheets (a = 1).

• Factor Trinomials (b>0, c>0).
• Factor Trinomials (b>0, c<0).
• Factor Trinomials (b<0, c>0).
• Factor Trinomials (b<0, c<0).
• Factor Trinomials (b & c can be positive or negative).

These are the steps to factor trinomials:

• Make sure the trinomial is written in standard form, which is in the form of ax 2 + bx + c, where a, b, and c are constants.
• Look for any common factors among the coefficients (a, b, and c) and factor them out. This step is important to simplify the trinomial before further factoring.
• Identify two numbers that multiply to give the constant term (c) and add up to give the coefficient of the middle term (b).
• Rewrite the middle term (bx) using the two numbers found in the previous step.
• Group the terms of the trinomial by grouping the first two terms and the last two terms.
• Factor out the greatest common factor (GCF) from each group, if possible.
• Apply the distributive property to factor out the common binomial factor.

Example: Factor the trinomial x 2 - 6x + 5.

• The trinomial is already in standard form.
• There are no common factors among the coefficients.
• The numbers that multiply to give 5 and add up to give -6 are -5 and -1.
• Rewrite the middle term: x 2 - 5x - x + 5
• Group the terms: (x 2 - 5x) + (-x + 5)
• Factor out the GCF from each group: x(x - 5) - 1(x - 5)
• Apply the distributive property: (x - 1)(x - 5)

Therefore, the factored form of the trinomial x 2 - 6x + 5 is (x - 1)(x - 5).

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Factor Trinomials Worksheets .

More Factor Trinomials Worksheets

Printable (Answers on the second page.) Factor Trinomials Worksheet #1 (b>0, c>0) Factor Trinomials Worksheet #2 (b>0, c<0) Factor Trinomials Worksheet #3 (b<0, c>0) Factor Trinomials Worksheet #4 (b<0, c<0) Factor Trinomials Worksheet #5 (b & c can be positive or negative)

Online or Generated Factor Binomials by Difference of Squares Factor Perfect Square Trinomials Factor Trinomials or Quadratic Equations Factor Different Types of Trinomials 1 Factor Different Types of Trinomials 2 Solve Trinomials using Quadratic Formula Find Discriminants of Quadratic Polynomials

Related Lessons & Worksheets

Factor Trinomials (Unfoil) Factor Trinomials (Grouping)

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Factoring Polynomials Worksheets

The factoring polynomials worksheets require a child to take the common factor or GCF out. The expressions deal with single as well as multiple variables.

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Factor Trinomials Worksheet and Answer Key

Students will practice how to factor trinomials . This sheet has model problems worked out, step by step. 25 scaffolded questions on factoring quadratic trinomials that start out relatively easy and end with some real challenges.

Example Questions

Directions Factor

Challenge Problems

Other Details

This is a 4 part worksheet:

• Part I Model Problems
• Part II Practice
• Part III Challenge Problems
• Part IV Answer Key
• Methods of Factoring

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