for the worths 8, 12, 20Solution through Factorization:The factors 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 typical factor is 4.

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## Calculator Use

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

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

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

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

## What is the Greatest common Factor?

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

## Greatest typical Factor that 0

Any non zero entirety number times 0 equates to 0 so it is true the every no zero entirety number is a variable 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 also 0 are components 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 find the Greatest common Factor (GCF)

There are several means to uncover the greatest usual factor of numbers. The most efficient technique you use relies on how numerous numbers friend have, how large they are and what you will do with the result.

### Factoring

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

Example: uncover the GCF that 18 and also 27

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

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

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

The greatest usual factor that 18 and 27 is 9.

Example: discover the GCF of 20, 50 and 120

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

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

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

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

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

### Prime Factorization

To discover the GCF by element factorization, list out all of the prime determinants of every number or discover them with a Prime determinants Calculator. Perform the prime factors that are typical to every of the initial numbers. Include the highest variety of occurrences of each prime aspect that is usual to each initial number. Main point these with each other to gain the GCF.

You will check out that as numbers acquire larger the prime factorization an approach may be much easier than directly factoring.

Example: find the GCF (18, 27)

The element factorization of 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 determinants of 18 and 27 are 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 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 of 120 is 2 x 2 x 2 x 3 x 5 = 120.

The incidents of common prime factors of 20, 50 and also 120 space 2 and 5.

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

### Euclid"s Algorithm

What carry out you carry out if you want to find the GCF of more than 2 very big 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 shown above. But if you need to do the administer by hand it will be a many work.

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

given two whole numbers, subtract the smaller sized number from the bigger number and note the result. Repeat the procedure subtracting the smaller number native the result until the an outcome is smaller sized than the original tiny number. Usage the original small number together the brand-new larger number. Subtract the an outcome from step 2 native the brand-new larger number. Repeat the process for every brand-new larger number and also 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 added information see 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 result 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 various other words, the GCF the 3 or an ext numbers deserve to be discovered by recognize the GCF that 2 numbers and also using the an outcome along with 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 common factor the 120 and also 50 is 10.

Now let"s uncover the GCF the our third value, 20, and our result, 10. GCF (20,10)

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

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

Therefore, the greatest usual factor the 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 common factor the 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 typical factor of 177 and also 137688 is 3.

Therefore, the greatest common factor of 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 web Resource.