GCF Calculator

How GCF calculator works?

Greatest common divisor calculator let you calculate the GCF with great comfort. To use this GCD calculator:

Step 1: Enter the numbers in the input box.

Step 2: Separate each number by using a comma.

Step 3: Select a method from the dropdown list.

Step 4: Click on the Calculate button to get the GCF.

Note: Binary (Stein’s) algorithm and upside down division method can only find the GCF of two numbers. If you want to find the greatest common factor of more than 2 numbers, you can select other methods listed in the GCF finder.

GCF definition - What is GCF?

Greatest common factor definition can be stated as GCF is the largest number that can divide two or more numbers. It is the highest number in all common factors of two or more numbers.
GCF is denoted as:
GCF (12, 16) = 4

How to find the greatest common factor?

You might be wondering how to find the GCF without using the greatest common denominator calculator. As discussed above, there are multiple methods to find the greatest common divisor. We will explore each of them one by one with examples.

Examples

Find the GCF of 8, 10, and 12

Solution

1. List of Factors

In list of factors method, we list all the factors of given numbers and find the common factors among them.

Step 1:

List all factors of 8, 10, and 12
8 = 1, 2, 4, 8
10 = 1, 2, 5, 10
12 = 1, 2, 3, 4, 6, 12

Step 2:

Highlight all common factors.
8 = 1, 2, 4, 8
10 = 1, 2, 5, 10
12 = 1, 2, 3, 4, 6, 12
1 and 2 are common factors in the factors of 8, 10 and 12. So, 2 is the greatest common number in all common factors.
GCD (8, 10, 12) = 2

2. Prime Factorization

In the prime factorization method, we list the prime factors of all numbers. Then, multiply all common factors to get the GCF.

Step 1:

Find the prime factors of all numbers using long division.

Step 2:

List all prime factors, highlight the common number. Multiply them if there is more than one common number.
8 = 2, 2, 2
10 = 2, 5
12= 2, 2, 3
In this case, there is only one common number which is 2.
So, the greatest common multiple of 8, 10 and 12 is 2.

3. Division step method

In the division step method, we divide the largest number with the smallest number. Use the remainder as the divisor and the previous divisor as a dividend. Continue dividing this way until the remainder is 0.

Step 1:

Divide the greatest number by the smallest number using steps.

Step 2:

Take the 3^rd number 10 as dividend and the common factor of 8 and 12 which is 4 as the divisor. Continue this step if there are more numbers in your calculation.

GCD (8, 10, 12) = 2
You can also verify the GCF using continuous division calculator above.

4. Euclidean algorithm

Step 1:

Arrange the numbers in ascending order
8, 10, 12

Step 2:

Divide all numbers with the smallest number. Use modulo operation % to get the remainders.
10 mod 8 = 2
12 mod 8 = 4

Step 3:

Take the divisor and remainders and arrange them in ascending order
2, 4, 8

Step 4:

Repeat the previous step for 2, 4, and 8 (Take the modulo of the numbers with the smallest one).
4 mod 2 = 0
8 mod 2 = 0

Step 5:

Again take the divisor and remainders and arrange them in ascending order.
0, 0, 2 →2
You can see, there is only one number left which is 2. So the greatest common divisor is 2.

5. Binary (Stein's) algorithm

Step 1:

Arrange the numbers in ascending order and assume initial GCF is 1.
8, 10, 12
GCF = 1

Step 2:

Divide all numbers by 2 and multiply initial GCF by 2.
8/2, 10/2, 12/2
4, 5, 6
GCF = 1 x 2 = 2

Step 3:

If there are any even values remaining, divide them by 2 and repeat this step until there are no even values.
4/2, 5, 6/2
2, 5, 3
Dividing again...
2/2, 5, 3
1, 5, 3

Step 4:

Arrange the numbers in ascending order and remove duplicate values.
1, 3, 5
Pick the first number, which is 1. As the only common factor of the remaining numbers is 1, there is no change to the GCF.
Hence, the Greatest Common Factor of 8, 10, and 12 is 2.

6. Upside down division/Ladder

Upside down division method or ladder method only calculates GCF of two values. That is why, we will use only two value 8 and 10 in this method.

Step 1:

Write both numbers next to each other.

Step 2:

Divide both numbers with a prime number that can divide both of them completely (without remainder).
We will divide 8 and 10 with 2. Write the quotient underneath the dividend,

So, 2 is the greatest common factor of 8 and 10.

GCF Examples