1141 LearnersLast updated on June 6th, 2025
Greatest Common Factor
The factors of a number are the numbers that can evenly divide the given number. GCF is the greatest common factor of two or more numbers. It is defined as the largest number that divides two or more numbers evenly. To learn GCF, it is important to know the difference between dividend and a divisor. While dividend is the number that gets divided, divisor is the number by which we divide the dividend.
What is the Greatest Common Factor (GCF)?
GCF is the greatest common factor of two or more numbers. In other words, GCF of two numbers is the largest number that divides the given numbers without leaving a remainder. There are different methods to find the GCF of any number, like listing out the common factors, prime factorization, and the division method.
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What is a Factor?
Factors are numbers that divide the given number evenly. For instance, the factors of 12 are 1, 2, 3, 4, 6, and 12. Common factors are the factors that are common in any two or more numbers. For example, the common factors of 12 and 24 are 1, 2, 3, 4, 6, and 12.
What is the Difference Between LCM and GCF?
LCM and GCF are the two fundamental concepts in mathematics. Now, let’s discuss the difference between LCM and GCF.
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How to Find the Greatest Common Factor?
In this section, let’s see how to find the GCF of any two or more numbers. The common methods used to find the GCF are:
- Listing Out Common Factors
- Prime Factorization
- Division Method
Listing Out Common Factors
In this method, we write down the factors of the given number and identify the common factors to find the GCF. Follow these steps to find the GCF of any two or more numbers using listing out common factors:
Step 1: Write down all the factors of the given number.
Step 2: Identifying the common factors from the list.
Step 3: The largest number from the common factors is the GCF.
Now, let’s find the GCF of 45 and 50
Step 1: List the factors of 45 and 50
The factors of 45 are 1, 3, 5, 9, 15, and 45
The factors of 50 are 1, 2, 5, 10, 25, and 50
Step 2: Identify the common factors from the list.
The common factors of 45 and 50 are 1 and 5
Step 3: Find the largest number among the common factors
Here, the largest common factor is 5
So, the GCF of 45 and 50 is 5
Prime Factorization
In this method, the given number is broken down into its prime factors. Then the common prime factors are identified and multiplied to determine the GCF. Follow the steps mentioned below to find the GCF:
Step 1: Breaking the given number into its prime factors
Step 2: Identify the common prime
Step 3: Multiplying the common prime factors
Now, let’s find the GCF of 45 and 50
Step 1: Breaking the given number into its prime factors
The prime factorization of 45 is 3 × 3 × 5
The prime factorization of 50 is 2 × 5 × 5
Step 2: Identifying the common prime
The common prime factor is 5
Step 3: Multiplying the common prime factors
As 5 is the only prime factor of 45 and 50, the GCF of 45 and 50 is 5.
Division Method
In this method, we divide the larger number by its smaller counterpart. Then the remainder is divided by the previous divisor. The process is repeated until the remainder is zero. Follow the steps given below to find the GCF using the division method:
Step 1: Dividing the largest number by the smallest number
Step 2: If the remainder is 0 in the first step, then the divisor in step 1 will be the dividend in step 2. Now, the remainder will be the new divisor.
Step 3: When the remainder becomes 0, the divisor will be the GCF. If not, the process will be repeated.
Now, let’s find the GCF of 45 and 50
Step 1: Dividing the largest number by the smallest number. So dividing 50 by 45, then the leftover is 5
Step 2: As the leftover is 5, now 45 will be the dividend and 5 will be the divisor, and here the remainder is 0
Step 3: Now the remainder is 0, so the GCF of 45 and 50 is 5.
Common Mistakes and How to Avoid Them in Greatest Common Factor
The largest number is a common factor among them, and it is the GCF of the numbers. Now, let’s learn a few common mistakes and the ways to avoid them in the GCF.
Mistake 1
Confusing GCF with LCM
Students often get confused between GCF and LCM as both are kind of similar concepts. So, it is important to understand the difference between the GCF and LCM. GCF is the largest common factor among the given numbers, and LCM is the smallest common multiple among the numbers.
Mistake 2
Missing out the factors in listing out common factors method
While listing out the common factors among the given numbers to find GCF, students forget to list all the factors, which can lead to errors. Missing one factor can lead to an error in GCF, so it is important to list out all the factors and double-check the answer before finding the GCF.
Mistake 3
Incorrect prime factorization
While employing the prime factorization method, students tend to make mistakes in breaking down the number into its prime numbers. Therefore, always double-check the steps involved in prime factorization.
Mistake 4
Errors in the division method
In the division method, the students misidentify the quotient, divisor, and dividend. So it is important to understand what the quotient, divisor, and dividend means. Before using the division method to find the GCF.
Mistake 5
Thinking that the number with GCF as 1 must be prime
Students tend to think only the prime numbers have GCF as 1, but it's not correct. As even composite numbers also have GCF of 1, for example 8 and 15.
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Solved Examples of Greatest Common Factor
Problem 1
Emma has 24 red beads and 36 blue beads. She wants to arrange them in identical groups with the same number of each type of bead in every group. What is the greatest number of groups she can make?
The greatest number of groups Emma can make is 12
Explanation
To find the greatest number of groups Emma can make, we need to calculate the GCF of 24 and 36
Listing out all the factors of 24 and 36
Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
List all the common factors between 24 and 36. I.e., 1, 2, 3, 4, 6, 12.
Therefore, the Greatest Common Factor (GCF) is 12.
Problem 2
A baker has 42 chocolate muffins and 56 vanilla muffins. He wants to place them in the largest possible identical boxes without mixing the flavors. How many muffins will be in each box?
Each box has 12 muffins
Explanation
For each number, find the prime factorization
The Prime Factorization of 42 is 2 × 3 × 7
The Prime Factorization of 56 is 2 × 2 × 2 × 7.
Find the Common Prime Factors between 42 and 56 then multiply them
I.e., 2, 7 = 2 × 7 = 14.
Therefore, the Greatest Common Factor of 42 and 56 is 14.
Problem 3
A school is distributing 48 pencils and 72 erasers to students. Each student should receive the same number of pencils and erasers. What is the maximum number of students that can receive supplies?
the maximum number of students that can receive is 24
Explanation
To find the maximum number of students that can receive the supplies can be found by finding the GCF of 48 and 72
Find the GCF of 48 and 72 using division method
Dividing the larger number by the smaller that is 72 ÷ 48, here the remainder is 24. When we divide 48 by 24, the remainder is 0. So the GCF is 24.
Problem 4
A gardener has 90 rose plants and 60 tulip plants. He wants to plant them in equal rows. What is the greatest number of rows he can make?
The greatest number of rows the gardener can make is 30
Explanation
To find the greatest number of rows, we can find the GCF of 90 and 60
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Here, the common factors are 1, 2, 3, 5, 6, 10, 15, and 30
So, the GCF (60, 90) is 30
Problem 5
A farmer has 50 cows and 75 sheep. He wants to group them in the largest possible, equal-sized herds. What is the largest number of animals in each herd?
The largest number of animals in each herd is 25
Explanation
To find the largest number of animals in each herd, we should determine the GCF of 50 and 75. So, let us find the prime factorization of 50 and 75.
The prime factorization of 50 is 2 × 5 × 5 = 2 × 52
The prime factorization of 75 is 3 × 5 × 5 = 3 × 52
So, the GCF of 50 and 75 is 52 = 5 × 5 = 25
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FAQs on Greatest Common Factor
1.What is GCF?
2.What is the GCF of 60 and 66?
3.What is the GCF of 18 and 24?
4.What is the GCF of 18 and 45?
5.What is the GCF of 24 and 36?
6.How can children in Bahrain use numbers in everyday life to understand Greatest Common Factor?
7.What are some fun ways kids in Bahrain can practice Greatest Common Factor with numbers?
8.What role do numbers and Greatest Common Factor play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Greatest Common Factor skills?
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