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

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

Enter 2 or much more whole number separated through commas or spaces.

The Greatest typical Factor Calculator solution likewise works as a equipment for finding:

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

## What is the Greatest common Factor?

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

## Greatest typical Factor the 0

Any no zero totality number times 0 amounts to 0 so it is true the every non zero entirety number is a element of 0.

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

For example, 5 × 0 = 0 so that is true the 0 ÷ 5 = 0. In this example, 5 and also 0 are factors 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 find the Greatest usual Factor (GCF)

There are several ways to find the greatest common factor the numbers. The many efficient an approach you use counts on how countless numbers friend have, how big they are and what friend will do with the result.

### Factoring

To uncover the GCF through factoring, list out every one of the determinants of every number or find them through a determinants Calculator. The whole number components are number that division evenly into the number through zero remainder. Provided the perform of usual factors because that each number, the GCF is the largest number usual to every list.

Example: find the GCF the 18 and also 27

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

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

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

The greatest typical 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 determinants of 50 space 1, 2, 5, 10, 25, 50.

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

The common factors the 20, 50 and also 120 room 1, 2, 5 and also 10. (Include just the factors usual to all 3 numbers.)

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

### Prime Factorization

To uncover the GCF by element factorization, list out every one of the prime components of each number or find them through a Prime determinants Calculator. List the prime factors that are common to every of the original numbers. Encompass the highest number of occurrences of each prime aspect that is usual to each original number. Main point these together to acquire the GCF.

You will view that as numbers get larger the prime factorization an approach may be much easier than directly factoring.

Example: uncover the GCF (18, 27)

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

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

The occurrences of usual prime factors of 18 and also 27 are 3 and 3.

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

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

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

The prime factorization that 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 occurrences of usual prime factors of 20, 50 and also 120 room 2 and also 5.

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

### Euclid"s Algorithm

What perform you carry out if you desire to uncover the GCF of much more than 2 very big numbers such as 182664, 154875 and 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 need to do the administrate by hand it will be a the majority of work.

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

provided two totality numbers, subtract the smaller sized number indigenous 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 together the brand-new larger number. Subtract the result from action 2 native the brand-new larger number. Repeat the procedure for every brand-new larger number and smaller number until you reach zero. Once you with zero, go back one calculation: the GCF is the number you found just prior to the zero result.

For extr information see our Euclid"s Algorithm Calculator.

Example: discover the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

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

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

Note the the GCF (x,y,z) = GCF (GCF (x,y),z). In various other words, the GCF that 3 or much more numbers deserve to be uncovered by finding the GCF of 2 numbers and using the result along through the next number to uncover the GCF and so on.

Let"s acquire 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 also 50 is 10.

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

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

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

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

Example: discover 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 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 common factor of 177 and 137688 is 3.

Therefore, the greatest common factor the 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." native MathWorld--A Wolfram internet Resource.