for the values 8, 12, 20Solution through Factorization:The components of 8 are: 1, 2, 4, 8The components of 12 are: 1, 2, 3, 4, 6, 12The factors of 20 are: 1, 2, 4, 5, 10, 20Then the greatest common factor is 4.

You are watching: Greatest common factor of 9 and 36  ## Calculator Use

Calculate GCF, GCD and HCF the a set of 2 or more numbers and see the work-related using factorization.

Enter 2 or an ext whole numbers separated through commas or spaces.

The Greatest typical Factor Calculator solution likewise works as a systems for finding:

Greatest common factor (GCF) Greatest typical denominator (GCD) Highest typical factor (HCF) Greatest typical divisor (GCD)

## What is the Greatest usual Factor?

The greatest typical factor (GCF or GCD or HCF) of a set of entirety numbers is the biggest positive integer the divides evenly into all numbers with zero remainder. Because that example, because that the collection of number 18, 30 and 42 the GCF = 6.

## Greatest usual Factor that 0

Any no zero whole number time 0 equals 0 so the is true that every non zero entirety number is a element of 0.

k × 0 = 0 so, 0 ÷ k = 0 for any type of whole number k.

For example, 5 × 0 = 0 so it is true that 0 ÷ 5 = 0. In this example, 5 and 0 are components of 0.

GCF(5,0) = 5 and an ext generally GCF(k,0) = k for any whole number k.

However, GCF(0, 0) is undefined.

## How to find the Greatest common Factor (GCF)

There are several ways to find the greatest usual factor that numbers. The many efficient method you use relies on how many numbers girlfriend have, how large they are and what you will carry out with the result.

### Factoring

To discover the GCF through factoring, perform out all of the determinants of every number or discover them with a determinants Calculator. The entirety number factors are numbers that division evenly right into the number v zero remainder. Offered the list of common factors for each number, the GCF is the largest number usual to each list.

Example: uncover the GCF the 18 and 27

The determinants of 18 room 1, 2, 3, 6, 9, 18.

The factors of 27 room 1, 3, 9, 27.

The usual factors of 18 and also 27 are 1, 3 and also 9.

The greatest common factor the 18 and also 27 is 9.

Example: uncover the GCF the 20, 50 and 120

The components of 20 room 1, 2, 4, 5, 10, 20.

The components of 50 are 1, 2, 5, 10, 25, 50.

The factors of 120 space 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.

The usual factors the 20, 50 and 120 room 1, 2, 5 and also 10. (Include just the factors common to all three numbers.)

The greatest typical factor the 20, 50 and 120 is 10.

### Prime Factorization

To find the GCF by element factorization, list out every one of the prime determinants of every number or discover them through a Prime components Calculator. Perform the prime determinants that are usual to each of the original numbers. Incorporate the highest number of occurrences of every prime aspect that is usual to each original number. Multiply these together to get the GCF.

You will see that as numbers obtain larger the element factorization method may be much easier than directly factoring.

Example: find the GCF (18, 27)

The prime factorization of 18 is 2 x 3 x 3 = 18.

The prime factorization the 27 is 3 x 3 x 3 = 27.

The cases of common prime components of 18 and 27 are 3 and also 3.

So the greatest usual factor the 18 and also 27 is 3 x 3 = 9.

Example: find the GCF (20, 50, 120)

The prime factorization that 20 is 2 x 2 x 5 = 20.

The element factorization of 50 is 2 x 5 x 5 = 50.

The prime factorization the 120 is 2 x 2 x 2 x 3 x 5 = 120.

The events of common prime factors of 20, 50 and also 120 room 2 and 5.

So the greatest typical factor of 20, 50 and also 120 is 2 x 5 = 10.

### Euclid"s Algorithm

What do you execute if you desire to uncover the GCF of an ext than 2 very large numbers such as 182664, 154875 and also 137688? It"s easy if you have a Factoring Calculator or a element Factorization Calculator or also the GCF calculator presented above. Yet if you must do the administer by hand it will certainly be a the majority of work.

## How to discover the GCF making use of Euclid"s Algorithm

given two entirety numbers, subtract the smaller number from the larger number and note the result. Repeat the process subtracting the smaller sized number native the result until the result is smaller than the original small number. Use the original little number together the brand-new larger number. Subtract the result from action 2 from the new larger number. Repeat the process for every new larger number and also smaller number till you reach zero. When you with zero, go back one calculation: the GCF is the number you found just prior to the zero result.

For additional information view our Euclid"s Algorithm Calculator.

Example: uncover the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

So, the greatest usual factor the 18 and also 27 is 9, the smallest an outcome we had prior to we reached 0.

Example: find the GCF (20, 50, 120)

Note the the GCF (x,y,z) = GCF (GCF (x,y),z). In various other words, the GCF the 3 or much more numbers deserve to be uncovered by detect the GCF the 2 numbers and also using the an outcome along with the next number to uncover the GCF and also so on.

Let"s get the GCF (120,50) first

120 - 50 - 50 = 120 - (50 * 2) = 20

50 - 20 - 20 = 50 - (20 * 2) = 10

20 - 10 - 10 = 20 - (10 * 2) = 0

So, the greatest common factor the 120 and 50 is 10.

Now let"s find the GCF of our 3rd value, 20, and also our result, 10. GCF (20,10)

20 - 10 - 10 = 20 - (10 * 2) = 0

So, the greatest common factor of 20 and also 10 is 10.

Therefore, the greatest common factor that 120, 50 and also 20 is 10.

Example: discover the GCF (182664, 154875, 137688) or GCF (GCF(182664, 154875), 137688)

First we uncover the GCF (182664, 154875)

182664 - (154875 * 1) = 27789

154875 - (27789 * 5) = 15930

27789 - (15930 * 1) = 11859

15930 - (11859 * 1) = 4071

11859 - (4071 * 2) = 3717

4071 - (3717 * 1) = 354

3717 - (354 * 10) = 177

354 - (177 * 2) = 0

So, the the greatest typical factor of 182664 and 154875 is 177.

Now we find the GCF (177, 137688)

137688 - (177 * 777) = 159

177 - (159 * 1) = 18

159 - (18 * 8) = 15

18 - (15 * 1) = 3

15 - (3 * 5) = 0

So, the greatest usual factor of 177 and 137688 is 3.

Therefore, the greatest common factor that 182664, 154875 and also 137688 is 3.

### References

<1> Zwillinger, D. (Ed.). CRC typical Mathematical Tables and Formulae, 31st Edition. New York, NY: CRC Press, 2003 p. 101.

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<2> Weisstein, Eric W. "Greatest typical Divisor." from MathWorld--A Wolfram web Resource.