What is the Greatest Common Factor?
The Greatest Common Factor (GCF) is the largest number that divides two or more whole numbers evenly. In other words, it's the largest number that can divide both numbers without leaving any remainder. GCF is also known as the Greatest Common Divisor (GCD).
How to find the GCF
To find the GCF of two or more numbers, follow these steps:
Step 1: List the factors of each number.
Factors are the numbers that can divide a given number without leaving a remainder.
Step 2: Identify the common factors.
Common factors are the factors that are shared between the given numbers.
Step 3: Determine the Greatest Common Factor (GCF).
The GCF is the largest number among the common factors.
Finding the GCF in an example
Here’s an example to make it clearer.
Let's find the GCF of 24 and 36.
Step 1: List the factors of each number.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Step 2: Identify the common factors.
Common factors of 24 and 36: 1, 2, 3, 4, 6, 12
Step 3: Determine the Greatest Common Factor (GCF).
The GCF of 24 and 36 is 12 because it is the largest number among the common factors.
So, the Greatest Common Factor of 24 and 36 is 12.
In some cases, the numbers might not have any common factors other than 1 (except for 1 itself). In such cases, the Greatest Common Factor would be 1 since every number is divisible by 1.
In our grade 6 math section, we have several worksheets for students to practice GCF.
Greatest common factor worksheets
These worksheets have students practice finding the GCF of two numbers within 2 – 50.
GCF of two numbers worksheets
These worksheets have students find the GCF of two numbers within 2 – 100.
Practice GCF of three numbers
These worksheets ask students to work out the GCF of three numbers.
