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

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## Calculator Use

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

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

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

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

## What is the Greatest usual Factor?

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

## Greatest typical Factor that 0

Any non zero whole number times 0 equals 0 so that is true the every no zero whole number is a aspect of 0.

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

For example, 5 × 0 = 0 so it 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 type of whole number k.

However, GCF(0, 0) is undefined.

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

There space several means to uncover the greatest usual factor of numbers. The many efficient method you use counts on how numerous numbers girlfriend have, how huge they are and also what friend will perform with the result.

### Factoring

To uncover the GCF by factoring, perform out every one of the components of each number or find them with a components Calculator. The entirety number components are number that divide evenly right into the number v zero remainder. Provided the list of usual factors for each number, the GCF is the largest number common to every list.

Example: uncover the GCF the 18 and also 27

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

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

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

The greatest typical factor of 18 and 27 is 9.

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

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

The factors of 50 space 1, 2, 5, 10, 25, 50.

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

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

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

### Prime Factorization

To uncover the GCF by element factorization, perform out every one of the prime components of each number or find them v a Prime components Calculator. Perform the prime components that are typical to every 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 gain the GCF.

You will view that as numbers obtain larger the element factorization method may be easier than straight factoring.

Example: uncover the GCF (18, 27)

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

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

The events of common prime determinants of 18 and also 27 space 3 and 3.

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

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

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

The element factorization the 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 cases of typical prime components of 20, 50 and also 120 space 2 and also 5.

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

### Euclid"s Algorithm

What perform you execute if you desire to uncover the GCF of an ext than two very huge numbers such as 182664, 154875 and also 137688? It"s basic if you have actually a Factoring Calculator or a prime Factorization Calculator or also the GCF calculator displayed above. But if you need to do the factorization by hand it will certainly be a most work.

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

given two entirety numbers, subtract the smaller sized number from the bigger number and note the result. Repeat the procedure subtracting the smaller sized number indigenous the result until the an outcome is smaller sized than the original small number. Use the original little number as the new larger number. Subtract the an outcome from action 2 native the new larger number. Repeat the process for every new larger number and smaller number until you with zero. Once you with zero, go earlier one calculation: the GCF is the number you found just prior to the zero result.

For added information view our Euclid"s Algorithm Calculator.

Example: uncover the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

So, the greatest common factor of 18 and 27 is 9, the smallest an outcome we had before we got to 0.

Example: discover 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 much more numbers deserve to be discovered by recognize the GCF the 2 numbers and also using the result along with the following number to find the GCF and so on.

Let"s gain 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 of 120 and 50 is 10.

Now let"s uncover the GCF that our 3rd value, 20, and 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 common factor of 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 typical factor of 182664 and 154875 is 177.

Now we discover 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 typical factor that 177 and 137688 is 3.

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

### References

<1> Zwillinger, D. (Ed.). CRC traditional Mathematical Tables and Formulae, 31st Edition. 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.