**Created By :**
Jatin Gogia

**Reviewed By :**
Rajasekhar Valipishetty

**Last Updated :**
Apr 06, 2023

**GCF of two numbers Calculator: **You can find GCF of two numbers using the GCF Calculator. The Greatest Common Factor Calculator over here can be quite handy for you to know the GCF of two numbers easily. Give the first input in the number 1 field and then second input in the number 2 field and press on the ‘Calculate’ button which is colored in blue. Remember not to use commas within your numbers like** 5,000, 7,500.**

**Ex: **GCF of 44 and 60 (or) GCF of 45 and 30 (or) GCF of 32 and 48

**Here are some samples of GCF of two numbers calculations.**

Related Calculators:

In Mathematics, Greatest Common Factor or Greatest Common Divisor of two numbers is the largest integer by which both the integers can be divided.

For instance, if you take the numbers 32, 256 the GCF of them would be 32 as it is the largest number that divides exactly both the given numbers.

GCF(32, 256) = 32

There are a number of ways in which you can find the Greatest Common Factor. However, which method would be appropriate will mostly depend on the numbers you are having, how large they are, and what you are going to do with the result.

There are three major methods by which you can find the GCF of numbers and they are as follows

Let’s get deep into each of the method by taking enough examples so that you will understand the concept of the Greatest Common Factor of two numbers easily.

In order to find GCF of two numbers using Factoring list out all factors of each number. Whole number factors are those that divide the number evenly leaving a remainder zero. Once you know the list of common factors GCF is the largest number common in each of the list.

**Example**

Find the GCF of numbers 36 and 45?

**Solution: **

Given numbers are 36 and 45

List of Positive Integers for the number 36 leaving a remainder zero is 1, 2, 3, 4, 6, **9**, 18, 36

List of Positive Integers for the number 45 leaving a remainder zero is 1, 3, 5, **9**, 15, 45

Greatest Common Factor of (36,45) that is largest and common in both the factors is 9.

Thus, GCF of 36, 45 is **9.**

In order to find the GCF of numbers using the prime factorization method list the prime factors of each number. List the Prime numbers that are common to each of the numbers. Include the highest number of occurrences of each prime number common to each original number. Multiply them to get the Greatest Common Factor.

You will find prime factorization easier compared to the factoring method when the numbers are large.

**Example**

Find the GCF of numbers 15, 45 using the Prime Factorization Method?

**Solution:**

Prime factorization of 15 is 3 x 5

Prime factorization of 45 is 3 x 3 x 5

The highest number of occurrences of each prime number common to each original number is 3*5 and on multiplying you will get the GCF as 15

GCF of (15,45) is **15**

If you want to find the GCF of two numbers using Prime Factorization and Factoring methods can be handy if the numbers are small. However, in the cases of large numbers factoring can be difficult. Euclid’s method of finding GCF can be a prime savior in such a case and eases your burden.

**Steps to find GCF using Euclid’s Algorithm**

- When given two numbers subtract the smaller number from the larger number and note the result.
- Continue the process subtracting the smaller number from the result until the result is smaller than the original smaller number.
- Use the original small number as a new large number and subtract the result you got in step from a new large number.
- Repeat the same process for every new large number and continue until you reach zero.
- Once you reach zero, go back to a step before and GCF is the number before the zero results.

**Example**

Find the GCF of (351,221) using Euclid’s Algorithm?

**Solution:**

In the given case numbers are 351, 221

Subtract the small number from the largest number i.e. 351 – 221 = 130

Subtract the result from the new large number i.e. 221 – 130 = 91

Repeat the same until you get zero i.e. 130 -91 = 39

Now it goes on further as such 91 – 39 = 52

and then 52 – 39 = 13

39 -13 = 26

26 -13 = 13

13 – 13 = 0

GCF is the number before the zero result and it is 13 in this case.

Thus, the GCF of (331, 221) is **13**.

Take the help of lcmgcf.com designed GCF Calculator and save your valuable time in calculating the lengthy greatest common factor of two numbers problems.

- GCF of 36 and 45
- GCF of 6 and 15
- GCF of 125 and 130
- GCF of 30 and 50
- GCF of 25 and 30
- GCF of 492 and 503
- GCF of 8 and 20
- GCF of 600 and 1050
- GCF of 44 and 46
- GCF of 10 and 15
- GCF of 360 and 792
- GCF of 28 and 42
- GCF of 40 and 48
- GCF of 24 and 30
- GCF of 12 and 20
- GCF of 300 and 310
- GCF of 45 and 63
- GCF of 14 and 28
- GCF of 27 and 36
- GCF of 28 and 35
- GCF of 4 and 8
- GCF of 6 and 9
- GCF of 16 and 32
- GCF of 192 and 200
- GCF of 36 and 42
- GCF of 117 and 135
- GCF of 36 and 72
- GCF of 24 and 60
- GCF of 6 and 12
- GCF of 18 and 30
- GCF of 12 and 48
- GCF of 2020 and 2021
- GCF of 54 and 72
- GCF of 126 and 130
- GCF of 168 and 180
- GCF of 54 and 60
- GCF of 7 and 14
- GCF of 252 and 258
- GCF of 8 and 16
- GCF of 6 and 10

- GCF of 45 and 51
- GCF of 42 and 54
- GCF of 20 and 32
- GCF of 24 and 40
- GCF of 24 and 28
- GCF of 90 and 108
- GCF of 18 and 72
- GCF of 40 and 60
- GCF of 20 and 40
- GCF of 20 and 30
- GCF of 15 and 24
- GCF of 18 and 27
- GCF of 100 and 105
- GCF of 132 and 150
- GCF of 160 and 168
- GCF of 27 and 45
- GCF of 21 and 35
- GCF of 42 and 56
- GCF of 150 and 160
- GCF of 804 and 306
- GCF of 13 and 30
- GCF of 288 and 292
- GCF of 60 and 66
- GCF of 10 and 18
- GCF of 21 and 30
- GCF of 5 and 20
- GCF of 60 and 75
- GCF of 10 and 30
- GCF of 33 and 45
- GCF of 120 and 180
- GCF of 400 and 420
- GCF of 96 and 100
- GCF of 210 and 225
- GCF of 360 and 365
- GCF of 15 and 21
- GCF of 16 and 18
- GCF of 180 and 200
- GCF of 42 and 63
- GCF of 7 and 13
- GCF of 144 and 150

**1. How do you find the GCF?**

You can find the GCF of numbers using any of the methods explained above. Depending on your comfort go with any of the three methods and find a solution.

**2. Where can I get numerous examples for finding GCF of two numbers?**

You can find the GCF of two numbers using various methods with examples from here.

**3. Where do I find a GCF Calculator that calculates GCF of numbers?**

You can find the GCF Calculator that calculates GCF of numbers from our page. Just give the inputs and you will find the Greatest Common Factor easily.