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 determinants 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 that a collection of two or much more numbers and also see the job-related using factorization.

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

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

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

## What is the Greatest common Factor?

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

## Greatest usual Factor of 0

Any non zero totality number time 0 equates to 0 so that is true the every no zero whole number is a element of 0.

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

For example, 5 × 0 = 0 so it is true that 0 ÷ 5 = 0. In this example, 5 and also 0 are components of 0.

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

However, GCF(0, 0) is undefined.

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

There room several means to discover the greatest typical factor of numbers. The many efficient technique you use relies on how numerous numbers friend have, how big they are and also what you will carry out with the result.

### Factoring

To find the GCF by factoring, perform out all of the determinants of each number or find them through a factors Calculator. The totality number determinants are number that division evenly right into the number with zero remainder. Provided the perform of typical factors for each number, the GCF is the biggest number usual to each list.

Example: uncover the GCF the 18 and 27

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

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

The common factors that 18 and also 27 room 1, 3 and 9.

The greatest usual factor of 18 and also 27 is 9.

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

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

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

The determinants of 120 space 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 space 1, 2, 5 and also 10. (Include only the factors common to all 3 numbers.)

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

### Prime Factorization

To discover the GCF by prime factorization, list out all of the prime determinants of each number or discover them with a Prime factors Calculator. List the prime factors that are usual to every of the initial numbers. Encompass the highest variety of occurrences of each prime aspect that is common to each original number. Main point these with each other to obtain the GCF.

You will view that together numbers get larger the prime factorization an approach may be less complicated than straight factoring.

Example: discover the GCF (18, 27)

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

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

The incidents of typical prime components 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: discover the GCF (20, 50, 120)

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

The prime factorization the 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 cases of common prime determinants of 20, 50 and 120 room 2 and also 5.

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

### Euclid"s Algorithm

What execute you perform if you want to uncover the GCF of more than 2 very large numbers such together 182664, 154875 and 137688? It"s simple if you have a Factoring Calculator or a element Factorization Calculator or even the GCF calculator displayed above. Yet if you should do the administer by hand it will certainly be a the majority of work.

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

provided two entirety numbers, subtract the smaller sized number indigenous the larger number and note the result. Repeat the process subtracting the smaller sized number indigenous the result until the an outcome is smaller than the original little number. Use the original small number together the brand-new larger number. Subtract the an outcome from step 2 indigenous the new larger number. Repeat the process for every brand-new larger number and smaller number until you reach zero. Once you with zero, go earlier one calculation: the GCF is the number you uncovered just prior to the zero result.

For extr information see our Euclid"s Algorithm Calculator.

Example: uncover the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

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

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

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

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

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

So, the greatest typical factor of 20 and 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 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 usual factor that 182664 and also 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 usual factor of 177 and 137688 is 3.

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

### References

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

See more: How Many Kilograms In 180 Pounds To Kilograms, 180 Lb To Kg

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