# Greatest Common Factor (GCF) – Definition, Formula, Examples | How to find Greatest Common Factor?

Greatest Common Factor (GCF) is the largest number and a factor of two or more numerical. These factors upon dividing results in natural numbers and they are essential to developing knowledge in multiplication and factors for attempting any equations in the future. Before going into the topic let us know what is Greatest Common Factor is? We are here to assist the students to enhance their knowledge of maths.

We will show different methods to solve the problems on Greatest Common Factor (GCF). GCF offers students a clear idea of the factors and multiples of each number. It also enables them to know which number is divisible and which isn’t. Learning Maths is always interesting. Know about Greatest Common Factor, GCF formula, how to find GCF of given two or more numbers, Example problems on GCF and so on from this article.

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### Greatest Common Factor (GCF) – Definition

The largest number, which is the factor of two or more given numbers is called Greatest Common Factor (GCF). The GCF of a number is the largest integer that can divide it without leaving a remainder. When you divide two numbers, you get certain common integers and among these factors, the Highest factor is GCF. The Greatest Common Factor is also known as the Highest Common Factor(HCF).

The above figure has clearly mentioned how to find the GCF of two given numbers. Consider an example for finding the GCF of a given number.

Example: Find the Greatest Common Factor of 16 and 24.
Solution: Given the values are 16 and 24.
The Factors of 16 are 1, 2, 4, 8, and 16.
The Factors of 24 are 1, 2, 3, 4, 6, 8, and 24.
Here, the numbers 1, 2, 4, 8 are common in both the factors of numbers.
Therefore, the greatest common factor of 16 and 24 is 8.
Thus, the GCF is 8.

### G.C.F Formula

G.C.F is simply Greatest Common Factor. Let a and b are two integers. The formula to find the Greatest Common Factor (GCF) of a and b is given as,
GCF(a, b) x L.C.M (a, b) = Product of two or more numbers.
GCF (a, b) = Product of two numbers / L.C.M (a, b).
Where L.C.M  is the Least Common Multiple.

### How to find Greatest Common Factor?

The process of finding the Greatest Common Factor or Highest factor is easy and requires students to be familiar with its formula. Students will need to have proper knowledge of multiplication and division for attempting these equations.

• To find out the GCF of two numbers, first, we will list the prime factors of each number.
• If both the numbers results have common factors it is GCF (Greatest Common Factor). If there are no common factors, the Greatest Common Factor of a given number is 1.

Finding the GCF of a number set can be very easy. However, there are many steps that need to be followed to get the correct Greatest Common Factor. In order to find the GCF of two given numbers, you need to find all the factors of both the numbers and then identify the common factors.

### Examples of Greatest Common Factor (GCF)

Example 1:
Find the GCF of 9 and 10.

Solution:
As given in the question, the values are 9 and 10.
Now, we will find the factors.
The factors of 9 are 1, 3, 9
The factors of 10 are 1, 2, 5
So, the common factor of given numbers is 1.
Hence, the HCF of 9 and 10 is 1.

Example 2:
Find the Greatest Common Factor of 40 and 72.

Solution:
Given the values are 40 and 72.
First, write the factors of given numbers,
The factors of 40 are 1, 2, 4, 5, 8, and 10.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12.
Now, write the Common factors of 40 and 72 are 1, 2, 4, 8. So, the greatest factor among them is 8.
Thus, the GCF of given numbers is 8.

Example 3:
Find the Greatest Common Factor of 12, 48.

Solution:
Given the values are 12 and 48.
First, we will write the factors of given numbers.
The factors of 12 are 1, 2, 3, 4, 6, and 12.
The factors of 48 are 1, 2, 3, 4, 6, 8, and 12.
Now, write the Common factors of 12 and 48 are 1, 2, 3, 4, 6, 12. So, the greatest factor among them is 12.
Thus, the GCF of the given numbers is 12.

Example 4:
What is the GCF of 39, 54, and 90?

Solution:
As given in the question, the values are 39, 54, and 90.
Now, we will write the factors.
The factors are 36 are 1, 2, 3, 4, 6, 8, 9,12, 18 and 39.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Thus, the common factors are 1, 3, 18.
Therefore, the Greatest Common factor of the given number is 18.

Example 5:
What is the Greatest Common Factor of 18, 28, 58, 68?

Solution:
Given, the GCF finding values are 18, 28, 58, and 68.
We will write the factors.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
The factors of 28 are 1, 2, 4, 7,14, and 28.
The factors of 58 are 1, 2, and 58.
The factors of 68 are 1, 2, 4, 17, and 68.
Now, write the common factors of 18, 28, 58, 68 is 1, 2.
Thus, the GCF of the given number is 2.

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### FAQ’s on Greatest Common Factor

1. What are the characteristics of GCF?

The Greatest number is a factor of two or more other numbers. When we find all the factors of two or more given numbers, and some factors are common, then the largest of those common factors is the Greatest Common Factor.

2. What is called GCF?

The Greatest Common Factor (GCF) or Greatest Common Divisor of a group of numbers is that the largest factor that every one the numbers share.

3. What is the difference between the HCF and GCF?

The HCF and GCF both are the same. There is no difference between HCF and GCD. Greatest Common Factor (GCF), Greatest Common Measure (GCM), and Highest Common Divisor all are the same.

4. Is GCF and LCM both are same?

LCM stands for Least Common Multiple. LCM of two numbers is the smaller value that is divisible by both two numbers. Whereas GCF is the highest common factor of two numbers, which can divide the two numbers evenly. Therefore, LCM and GCD are different.

5. Is GCD and HCF the same?

GCD is that the Greatest common divisor and HCF are that the Highest Common Factor. Both are the same.

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