Enter First Number:

Enter Second Number:

Greatest Common Factor (GCF):

GCF Calculator is a free online tool that displays the greatest common factor of two given numbers. BYJU’S online GCF calculator tool makes the calculation faster, and it displays the GCF in a fraction of seconds.

## What is GCF?

GCF or Greatest Common factor of two numbers is the value that can exactly divide the two numbers. Hence, there is no remainder left after division. GCF is also called HCF (Highest Common Factor) or GCD (Greatest Common Divisor).

For example, GCF of 36 and 54 is 18.

**How?**

Factors of 36 → 1, 2, 3, 4, 6, 9, 12, **18**, 36

Factors of 54 → 1, 2, 3, 6, 9, **18**, 27, 54

Hence, we can see here the greatest common factor is 18.

So, GCF (36, 54) = 18.

Now, to calculate the GCF quickly, you can use the calculator provided above and make your calculations faster.

## How to Use the GCF Calculator?

The procedure to use the GCF calculator is as follows:

**Step 1:** Enter two numbers in the respective input field

**Step 2:** Now click the button “Calculate GCF” to get the result

**Step 3:** Finally, the greatest common factor (GCF) will be displayed in the output field

### What is Meant by GCF?

In Mathematics, the Greatest Common Factor, abbreviated as GCF, is defined as the greatest number or the largest factor of two numbers. When the factors of two or more numbers are found, some numbers are found in common. The largest number of all those common factors is known as the greatest common factor (GCF).

For example, the GCF of two numbers 4 and 6 can be found as follows:

Factors of 4: 1, 2, 4

Factors of 6: 1, 2, 3, 6

Here, 2 is the largest number found in both factors. Hence, the GCF of 4 and 6 is 2.

## Examples

**1. GCF of 28 and 42 = 14**

Explanation:

Factors of 28 are: 1, 2, 4, 7, **14**, 28

Factors of 42 are: 1, 2, 3, 6, 7, **14**, 21, 42

Therefore, the greatest common factor is 14.

**2. GCF of 6 and 18 = 6**

Explanation:

The factors of 6 are: 1, 2, 3, **6**

The factors of 18 are: 1, 2, 3, **6**, 9, 18

Therefore, the greatest common factor is 6.

**3. GCF of 24 and 36 = 12**

Explanation:

Factors of 24 are: 1, 2, 3, 4, 6, 8, **12**, 24

Factors of 36 are: 1, 2, 3, 4, 6, 9, **12**, 18, 36

Therefore, the greatest common factor is 12.

**4. GCF of 36 and 45 = 9**

Explanation:

Factors of 36 are: 1, 2, 3, 4, 6, **9**, 12, 18, 36

Factors of 45 are: 1, 3, 5, **9**, 15, 45

Therefore, the greatest common factor is 9.

**5. GCF of 32 and 40 = 8**

Explanation:

Factors of 32 are: 1, 2, 4, **8**, 16, 32

Factors of 40 are: 1, 2, 4, 5, **8**, 10, 20, 40

Therefore, greatest common factor is 8

**6. GCF of 30 and 36**

Explanation:

Factors of 30 are: 1, 2, 3, 5, **6**, 10, 15, 30

Factors of 36 are: 1, 2, 3, 4, **6**, 9, 12, 18, 36

Therefore, greatest common factor is 6.

**7. GCF of 12 and 20 = 4**

Explanation:

Factors of 12 are: 1, 2, 3, **4**, 6, 12

Factors of 20 are: 1, 2, **4**, 5, 10, 20

Therefore, the greatest common factor is 4.

**8. GCF of 16 and 24 = 8**

Explantion:

Factors of 16 are: 1, 2, 4, **8**, 16

Factors of 24 are: 1, 2, 3, 4, 6, **8**, 12, 24

Therefore, the greatest common factor is 8.

**9. GCF of 36 and 48 = 12**

Explanation:

Factors of 36 are: 1, 2, 3, 4, 6, 9, **12**, 18, 36

Factors of 48 are: 1, 2, 3, 4, 6, 8, **12**, 16, 24, 48

Therefore, the greatest common factor is 12.