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

You are watching: Greatest common factor of three numbers  ## Calculator Use

Calculate GCF, GCD and HCF of a collection of 2 or much more numbers and see the work using factorization.

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

The Greatest usual Factor Calculator solution also works together a solution for finding:

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

## What is the Greatest common Factor?

The greatest common factor (GCF or GCD or HCF) of a collection of entirety numbers is the biggest positive integer the divides evenly into all numbers v zero remainder. For example, for the collection of numbers 18, 30 and 42 the GCF = 6.

## Greatest usual Factor that 0

Any non zero totality number times 0 equals 0 so the is true that every non zero totality number is a aspect of 0.

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

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

GCF(5,0) = 5 and much more generally GCF(k,0) = k for any whole number k.

However, GCF(0, 0) is undefined.

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

There room several methods to find the greatest usual factor of numbers. The most efficient method you use depends on how many numbers friend have, how huge they are and also what girlfriend will perform with the result.

### Factoring

To find the GCF by factoring, list out all of the determinants of each number or find them through a determinants Calculator. The entirety number components are number that division evenly into the number through zero remainder. Provided the perform of common factors for each number, the GCF is the largest number typical to each list.

Example: find the GCF the 18 and 27

The components of 18 are 1, 2, 3, 6, 9, 18.

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

The typical factors the 18 and 27 space 1, 3 and also 9.

The greatest usual factor of 18 and also 27 is 9.

Example: find the GCF of 20, 50 and 120

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

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

The components 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 typical to all 3 numbers.)

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

### Prime Factorization

To find the GCF by prime factorization, perform out every one of the prime components of each number or uncover them with a Prime factors Calculator. Perform the prime components that are usual to each of the initial numbers. Encompass the highest variety of occurrences of each prime variable that is usual to each initial number. Multiply these with each other to acquire the GCF.

You will check out that as numbers acquire larger the element factorization technique 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 incidents of usual prime components of 18 and also 27 space 3 and also 3.

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

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

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

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

The element factorization that 120 is 2 x 2 x 2 x 3 x 5 = 120.

The cases of typical prime determinants of 20, 50 and also 120 room 2 and 5.

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

### Euclid"s Algorithm

What execute you execute if you desire to uncover the GCF of much more than two very big numbers such as 182664, 154875 and 137688? It"s easy if you have a Factoring Calculator or a element Factorization Calculator or also the GCF calculator presented above. However if you must do the administer by hand it will certainly be a lot of work.

## How to uncover the GCF utilizing Euclid"s Algorithm

given two entirety numbers, subtract the smaller number native the larger number and note the result. Repeat the procedure subtracting the smaller number from the an outcome until the result is smaller sized than the original tiny number. Use the original small number as the new larger number. Subtract the an outcome from action 2 from the brand-new larger number. Repeat the process for every new larger number and smaller number until you reach zero. As soon as you with zero, go earlier one calculation: the GCF is the number you uncovered just before the zero result.

For additional information view our Euclid"s Algorithm Calculator.

Example: discover the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

So, the greatest typical factor of 18 and 27 is 9, the smallest result we had before we got to 0.

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

Note the the GCF (x,y,z) = GCF (GCF (x,y),z). In other words, the GCF that 3 or an ext numbers can be uncovered by finding the GCF that 2 numbers and also using the an outcome along v the next number to discover the GCF and also so on.

Let"s obtain 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 usual factor that 120 and also 50 is 10.

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

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

So, the greatest common factor that 20 and 10 is 10.

Therefore, the greatest usual factor of 120, 50 and 20 is 10.

Example: find 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 usual factor of 182664 and also 154875 is 177.

Now we uncover 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 common factor the 177 and 137688 is 3.

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

### References

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

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<2> Weisstein, Eric W. "Greatest common Divisor." indigenous MathWorld--A Wolfram internet Resource.