1119 LearnersLast updated on June 18th, 2025
Common Factors
A factor of a number is a number that divides the number evenly. Common factors of any two or more numbers are the numbers that can divide both numbers evenly. In this topic, we will learn more about common factors, how to find common factors, and GCF.
What are Common Factors?
The numbers that can evenly divide a number are known as factors of the number. For all the numbers, the number itself and 1 are the factors of the number.
The common factors of two or more numbers are the numbers that can evenly divide the numbers. When we compare any numbers, 1 will be a common factor.
For instance, the common factors of 6 and 8, the factors of 6 are 1, 2, 3, and 6, and the factors of 8 are 1, 2, 4, and 8. The common factors of 6 and 8 are 1 and 2.
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How to find common factors?
Now, let’s learn how to find the common factors of any two or more numbers. Follow these steps to find the common factors of any two or more numbers
Step 1: List all the factors of the given numbers
Step 2: Identify all the common numbers from the list; these are the common factors of the numbers.
Let’s find the common factors of 45 and 65
Step 1: Listing the factors of 45 and 65
The factors of 45: 1, 3, 5, 9, 15, 45
The factors of 65: 1, 5, 13, 65
Step 2: Here, the common factors are 1 and 5.
What is GCF?
The largest number from the common factors of the numbers is the GCF of the numbers. GCF stands for greatest common factor. That means the GCF of any number is the number that can divide the numbers evenly, that is, GCF(a, b) = x, and then x can evenly divide a and b.
For instance, let’s find the GCF of 45 and 65
The factors of 45: 1, 3, 5, 9, 15, 45
The factors of 65: 1, 5, 13, 65
Here, the common factors are 1 and 5
So, the GCF of 45 and 65 is 5
Real-world applications of Common Factors
The factors that are common among two or more numbers are the common factors of any number. In this section, let’s see how and why we use the common factors in real-life situations.
- In mathematics, we use common factors to find the GCF of any two or more numbers.
- When doing the basic operations in fractions, we use common factors to simplify the fraction and to find the common denominator
- For resource allocation, scaling models, electric circuits, manufacturing and production, etc, we use common factors in the field of engineering.
- To adjust the quantities of the recipe, we use common factors in cooking.
Common Mistakes and How to Avoid Them in Common Factors
Errors are common among students when solving the common factors, so let’s see some common mistakes and the ways to avoid them to master the common factors.
Mistake 1
Confusing factors with multiples
Students tend to mix up the factors and multiples of the numbers, thinking that 24 is a factor of 12, whereas it is a multiple of 12. So, students should understand the multiples and factors of a number. The multiple of a number is the product of multiplying the number with any other whole number, whereas the factor of a number is the number which can evenly divide the number.
Mistake 2
Not listing 1 and the number itself as factors
When listing the factors of a number, students forget to list the number itself and 1 as factors, which can lead to errors. 1, and the number itself is always a factor of the number.
For example, the factors of 16 are 1, 2, 4, 8, and 16.
Mistake 3
Not listing all the possible factors
Sometimes, students tend to stop listing the factors too early, so they miss listing a few factors, which leads to confusion. So, it is important to list all the factors of the numbers.
For instance, the factors of 40: 1, 2, 4, 5, 10, 40 (wrong) instead it should be written as 1, 2, 4, 5, 8, 10, 20, and 40
Mistake 4
Confusing prime and composite numbers
Students often tend to confuse prime and composite numbers. That is when listing the factors of numbers, that is, they think of 15 as a prime number and list 1 and 15 as its factors, which is wrong because 15 is not a prime number but a composite number.
Mistake 5
Incorrect identification of GCF
When identifying the GCF of any two numbers, students tend to make mistakes in identifying the common factor, that is, listing incorrect common factors or not listing all the factors. So, it is important to list all the factors and identify the common factors when finding the GCF of any two numbers.
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Solved Examples of Common Factors
Problem 1
Find the common factors of 12 and 18.
The common factors of 12 and 18 are 1, 2, 3, and 6
Explanation
The factors of 12 are 1, 2, 3, 4, 6, and 12
The factors of 18 are 1, 2, 3, 6, 9, and 18
So, the common factors are 1, 2, 3, and 6
Problem 2
Find the common factors of 20 and 30.
The common factors of 20 and 30 are 1, 2, 5, and 10
Explanation
The factors of 20 are 1, 2, 4, 5, 10, and 20
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30
So, the common factors are 1, 2, 5, and 10.
Problem 3
Find the common factors of 14 and 21
The common factors of 14 and 21 are 1 and 7
Explanation
The factors of 14 are 1, 2, 7, and 14
The factors of 21 are 1, 3, 7, and 21
So, the common factors are 1 and 7.
Problem 4
Find the common factors of 21, 35, and 49.
The common factors of 21, 35, and 49 are 1 and 7
Explanation
The factors of 21 are 1, 3, 7, and 21
The factors of 35 are 1, 5, 7, and 35
The factors of 49 are 1, 7, and 49
So, the common factors are 1 and 7.
Problem 5
Find the greatest common factors of 32 and 48.
The GCF of 32 and 48 is 16
Explanation
The factors of 32 are 1, 2, 4, 8, 16, and 32
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48
The common factors of 32 and 48 are 1, 2, 4, 8, 16
The GCF of 32 and 48 is 16
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FAQs on Common Factors
1.What are the common factors?
2.What are the common factors of 20 and 28?
3.What is GCF?
4.What is the GCF of 20 and 30?
5.Can a factor of a number be negative?
6.How can children in United Kingdom use numbers in everyday life to understand Common Factors?
7.What are some fun ways kids in United Kingdom can practice Common Factors with numbers?
8.What role do numbers and Common Factors play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Common Factors skills?
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
