The greatest common factor “GCF” is the highest number that divides two numbers. It is also known as the highest common factor “HCF”.
For example, the numbers 6, 18, and 24 have three common factors which are 2, 3, and 6. The highest number is 6.
So, the GCF of 6, 18, and 24 is 6.
How to find the GCF?
The GCF can be calculated by several methods. You can either find it by performing the manual calculations or by using different online GCF calculating tools.
In this article, we’ll discuss both ways of finding the greatest common factors in detail.
How to find GCF by using online tools?
If you’re tired of performing manual calculations, you can use different online calculating tools to find the HCF of multiple numbers.
The online GCF calculator finds the greatest common factor of several numbers by using different methods.
These calculators use the prime factorization, division, list of factors, and Euclidean algorithm methods to find the GCF in no time.
The best thing about these online tools is that they provide the complete step-by-step of every solution with one click.
The mentioned below platforms provides the best GCF calculators:
How to find GCF manually with Step by Step solution?
To find it manually, you can use the below methods:
1. Prime Factorization Method
To find the HCF by using this method, have a look at the below example.
Find the FCF of 12 and 18 by using the factorization method.
Step 1: Find the prime factor of all the following numbers.
Prime Factors of 12: 2 × 2 × 3
Prime Factors of 18: 2 × 3 × 3
Step 2: Identify each common prime factor.
The common prime factors of 18 and 24 are: 2, 3
Step 3: Multiply the common factors and the product of these common factors is the GCF of the given numbers.
2 × 3
So, the GCF of the mentioned above numbers is 6.
2. Division Method
To find the GCF by this method, follow the below example.
Find the HCF of 24 and 48 using the division method.
Step 1: Divide the highest number by the smallest number.
Step2: Take the divisor from the last step and further divide it with the reminder you get in the last step.
Step 3: Repeat the second step until the remainder becomes zero. The last divisor will be the greatest common factor.
So, the GCF of the above example is 24.
3. List of Factors Method
To find the highest common factor of different numbers by using this method, have a look at the below example:
Find the GCF of (12, 18, and 24) by using the list of factors method.
Step 1: Find all the factors of the given numbers.
Factors of 12 are 1, 2, 3, 4, 6, and 12.
Factors of 18 are 1, 2, 3, 6, 9, and 18.
Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.
Step 2: Find the highest common factor between all the common factors.
So, 6 is the GCF of 12, 18, and 24.