The GCF calculator evaluates the common factor of two or more numbers within seconds. Our most significant common factor calculator saves your time when dealing with big numbers.

## Greatest Common Factor:

In Mathematics,

**“The largest positive integer that can be divided evenly into two or more supplied numbers without leaving a remainder is referred to as the GCF"**

The greatest Common Factor is widely used to simplify fractions. The most significant common factor is also known as the Greatest common divisor.

## How To Find GCF?

If you are seeking how to find GCF, keep scrolling to go through the different __GCF formula__ methods:

### Methods To Find the GCF:

In the following section, we will provide you with examples to demonstrate all the methods one by one in an encyclopedic tone. Stay focused!

#### Factoring:

Factoring is the most valuable and regularly used method that is also used by this greatest common factor calculator.

##### Example:

We have two numbers, 15 & 35. Let’s estimate the Greatest common factor of these numbers.

###### Solution:

Factoring of 15 is = 1, 3, 5, 15

Factoring of 35 is = 1, 5, 7, 35

List all common factors 1 & 5, and the GCF is 5.

**Related: **Only use the factors algebra calculator for free to calculate factors.

#### Prime Factorization:

If you do not know how to do long division, then prime factorization is another choice to go by. It is almost the same as the above-explained method. Check it out briefly as under!

##### Example:

Suppose that we have two values, 10 & 65. Find GCF for the numbers by using prime factorization.

###### Solution:

The secondary method for the gcd calculator is Prime factorization.

The factors of 10 are = 1, 2, 5, 10

The factors of 65 are = 1, 5, 13, 65

So the GCF (10, 65) = 5

#### Euclidean Algorithm:

The Euclidean algorithm is another often-used method that may be considered by the gcd calculator to calculate accurate GCF.

**Statement: **

**“If C is the GCF of A & B, then C is also the GCF of the difference of A-B”**

##### Example:

Discover the GCF of 54 and 30 by using the Euclidean algorithm

###### Solution:

The difference of 54-30 equals 24.

GCF of 30-24 = 6

GCF of 24-6 =18

GCF of 18-6 =12

GCF of 12-6 = 6

GCF of 6-6 = 0

This helps to prove that the greatest common factor is the last non-zero number.

## Working of GCF Calculator:

The GCF finder determines the greatest common divisor instantly and precisely. The procedure for finding results is given below.

**Input:**

- Select the method of calculations
- Put the values in the respective field
- Then click the button “Calculate.”

**Output:**

The greater common factor calculator will give you the output as:

- GCF by the factoring way
- GCF by the prime factorization way
- GCF by the Euclidean algorithm

## References:

From the source Wikipedia: Greatest common divisor, Overview, Example, Applications, Calculation, Euclidean algorithm, Binary GCD algorithm, Complexity, Properties, Probabilities, and expected value

From the source Lumen Learning: The Greatest Common Factor