for the worths 8, 12, 20Solution through Factorization:The determinants 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 gcf of 5 and 6  ## Calculator Use

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

Enter 2 or much more whole number separated by 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 usual factor (HCF) Greatest usual divisor (GCD)

## What is the Greatest typical Factor?

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

## Greatest usual Factor of 0

Any non zero entirety number times 0 equates to 0 so that is true the every non zero totality number is a factor 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 factors of 0.

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

However, GCF(0, 0) is undefined.

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

There room several ways to uncover the greatest usual factor of numbers. The many efficient method you use depends on how plenty of numbers you have, how big they are and also what girlfriend will do with the result.

### Factoring

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

Example: uncover the GCF the 18 and also 27

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

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

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

The greatest common factor the 18 and 27 is 9.

Example: uncover the GCF the 20, 50 and 120

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

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

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

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

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

### Prime Factorization

To find the GCF by element factorization, list out all of the prime components of each number or discover them v a Prime determinants Calculator. Perform the prime determinants that are typical to each of the original numbers. Incorporate the highest variety of occurrences of every prime variable that is common to each original number. Multiply these together to acquire the GCF.

You will check out that as numbers get larger the prime factorization technique may be simpler than straight factoring.

Example: uncover the GCF (18, 27)

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

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

The incidents of typical prime determinants of 18 and also 27 space 3 and 3.

So the greatest typical factor the 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 element factorization of 50 is 2 x 5 x 5 = 50.

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

The events of typical prime factors of 20, 50 and 120 are 2 and also 5.

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

### Euclid"s Algorithm

What execute you carry out if you want to find the GCF of much more than two very large numbers such as 182664, 154875 and also 137688? It"s straightforward if you have a Factoring Calculator or a prime Factorization Calculator or even the GCF calculator presented above. But if you should do the administrate by hand it will be a the majority of work.

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

given two entirety numbers, subtract the smaller sized number from the larger number and also note the result. Repeat the procedure subtracting the smaller number from the result until the an outcome is smaller sized than the original little number. Usage the original tiny number as the new larger number. Subtract the result from action 2 indigenous the new larger number. Repeat the process for every new larger number and smaller number until you reach zero. As soon as you reach zero, go back one calculation: the GCF is the number you discovered just prior to the zero result.

For extr 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 the 18 and 27 is 9, the smallest an outcome we had prior to we reached 0.

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

Note that the GCF (x,y,z) = GCF (GCF (x,y),z). In other words, the GCF the 3 or much more numbers can be uncovered by detect the GCF that 2 numbers and also using the an outcome along v the following number to uncover 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 typical factor of 120 and also 50 is 10.

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

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

So, the greatest typical factor the 20 and also 10 is 10.

Therefore, the greatest typical 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 that 182664 and 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 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 common Divisor." from MathWorld--A Wolfram net Resource.