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 determinants of 20 are: 1, 2, 4, 5, 10, 20Then the greatest usual factor is 4.

You are watching: What is the greatest common factor of 8 and 6  ## Calculator Use

Calculate GCF, GCD and also HCF of a set of two or much more numbers and also see the work using factorization.

Enter 2 or more whole number separated by commas or spaces.

The Greatest common Factor Calculator solution additionally works as a equipment for finding:

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

## What is the Greatest typical Factor?

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

## Greatest typical Factor that 0

Any non zero entirety number time 0 amounts to 0 so it is true that every no zero entirety 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 the is true the 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 discover the Greatest typical Factor (GCF)

There space several ways to uncover the greatest typical factor that numbers. The many efficient an approach you use relies on how plenty of numbers friend have, how big they are and what girlfriend will carry out with the result.

### Factoring

To discover the GCF by factoring, list out every one of the components of every number or discover them v a components Calculator. The whole number components are number that division evenly into the number v zero remainder. Offered the perform of usual factors for each number, the GCF is the largest number typical to each list.

Example: find the GCF that 18 and 27

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

The determinants of 27 space 1, 3, 9, 27.

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

The greatest typical factor the 18 and 27 is 9.

Example: find the GCF of 20, 50 and also 120

The factors of 20 space 1, 2, 4, 5, 10, 20.

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

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

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

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

### Prime Factorization

To uncover the GCF by element factorization, perform out all of the prime determinants of every number or discover them v a Prime determinants Calculator. List the prime components that are common to every of the initial numbers. Include the highest variety of occurrences of each prime factor that is typical to each initial number. Main point these with each other to obtain the GCF.

You will view that together numbers gain larger the prime factorization technique may be simpler than right factoring.

Example: uncover the GCF (18, 27)

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

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

The events of typical prime components of 18 and also 27 are 3 and 3.

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

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

The element factorization of 20 is 2 x 2 x 5 = 20.

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

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

The occurrences of common prime components of 20, 50 and 120 are 2 and also 5.

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

### Euclid"s Algorithm

What do you carry out if you want to discover the GCF of more than 2 very huge numbers such together 182664, 154875 and 137688? It"s simple if you have a Factoring Calculator or a prime Factorization Calculator or even the GCF calculator shown above. But if you have to do the administer by hand it will be a many work.

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

provided two whole numbers, subtract the smaller number from the bigger number and note the result. Repeat the process subtracting the smaller sized number from the result until the result is smaller sized than the original tiny number. Use the original tiny number together the brand-new larger number. Subtract the an outcome from action 2 native the brand-new larger number. Repeat the process for every new larger number and smaller number until you with zero. When you reach zero, go back one calculation: the GCF is the number you discovered just prior to the zero result.

For additional information check out our Euclid"s Algorithm Calculator.

Example: uncover the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

So, the greatest common factor that 18 and also 27 is 9, the smallest an outcome we had before we reached 0.

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

Note that the GCF (x,y,z) = GCF (GCF (x,y),z). In various other words, the GCF the 3 or more numbers have the right to be found by recognize the GCF the 2 numbers and using the an outcome along v the following number to discover the GCF and 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 the 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 usual factor that 20 and also 10 is 10.

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

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

First we find 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 common 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 usual factor that 177 and also 137688 is 3.

Therefore, the greatest typical factor the 182664, 154875 and 137688 is 3.

### References

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

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