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

You are watching: What is the greatest common factor of 3, 24, and 27?  ## Calculator Use

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

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

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

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

## What is the Greatest typical Factor?

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

## Greatest usual Factor of 0

Any non zero entirety number times 0 equals 0 so the is true that every non zero totality number is a aspect of 0.

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

For example, 5 × 0 = 0 so the 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 discover the Greatest typical Factor (GCF)

There room several methods to discover the greatest usual factor that numbers. The many efficient method you use relies on how numerous numbers girlfriend have, how large they are and also what you will execute with the result.

### Factoring

To find the GCF through factoring, perform out all of the components of every number or uncover them with a determinants Calculator. The totality number components are numbers that division evenly right into the number v 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 that 18 and also 27

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

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

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

The greatest common factor the 18 and 27 is 9.

Example: uncover the GCF that 20, 50 and 120

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

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

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

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

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

### Prime Factorization

To find the GCF by element factorization, list out all of the prime factors of every number or uncover them v a Prime factors Calculator. Perform the prime factors that are common to every of the initial numbers. Include the highest variety of occurrences of each prime aspect that is usual to each initial number. Multiply these with each other to gain the GCF.

You will watch that together numbers acquire larger the prime factorization method may be simpler than straight factoring.

Example: find 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 typical prime components of 18 and also 27 are 3 and also 3.

So the greatest usual factor that 18 and 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 element factorization that 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 determinants of 20, 50 and 120 space 2 and 5.

So the greatest usual factor of 20, 50 and also 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 big numbers such together 182664, 154875 and 137688? It"s basic if you have a Factoring Calculator or a element Factorization Calculator or also the GCF calculator shown above. However if you need to do the factorization by hand it will be a most work.

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

given two entirety numbers, subtract the smaller sized number indigenous the larger number and also note the result. Repeat the procedure subtracting the smaller sized number from the result until the an outcome is smaller than the original tiny number. Usage the original tiny number together the new larger number. Subtract the an outcome from step 2 from the new larger number. Repeat the process for every brand-new larger number and also smaller number till you reach 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: find the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

So, the greatest typical factor that 18 and 27 is 9, the smallest result we had prior to we reached 0.

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

Note that the GCF (x,y,z) = GCF (GCF (x,y),z). In other words, the GCF of 3 or more numbers can be found by recognize the GCF that 2 numbers and also using the an outcome along v the next number to find 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 usual factor the 120 and 50 is 10.

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

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

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

Therefore, the greatest common factor that 120, 50 and 20 is 10.

Example: uncover the GCF (182664, 154875, 137688) or GCF (GCF(182664, 154875), 137688)

First we discover 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 common factor of 177 and also 137688 is 3.

Therefore, the greatest usual factor the 182664, 154875 and also 137688 is 3.

### References

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

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