for the values 8, 12, 20Solution by Factorization:The determinants of 8 are: 1, 2, 4, 8The factors 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.

You are watching: Greatest common factor of 18 and 27  ## Calculator Use

Calculate GCF, GCD and HCF the a set of 2 or an ext numbers and also see the occupational using factorization.

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

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

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

## What is the Greatest common Factor?

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

## Greatest typical Factor of 0

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

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

For example, 5 × 0 = 0 so the is true the 0 ÷ 5 = 0. In this example, 5 and 0 are determinants of 0.

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

However, GCF(0, 0) is undefined.

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

There space several means to find the greatest usual factor of numbers. The many efficient method you use depends on how plenty of numbers girlfriend have, how huge they are and what friend will execute with the result.

### Factoring

To discover the GCF by factoring, list out every one of the components of every number or discover them through a components Calculator. The entirety number factors are number that division evenly into the number through zero remainder. Provided the list of usual factors for each number, the GCF is the largest number common to each list.

Example: find the GCF the 18 and 27

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

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

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

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

Example: discover the GCF that 20, 50 and 120

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

The factors of 50 room 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 typical factors the 20, 50 and 120 space 1, 2, 5 and 10. (Include just the factors typical to all 3 numbers.)

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

### Prime Factorization

To uncover the GCF by element factorization, perform out all of the prime determinants of each number or discover them through a Prime factors Calculator. List the prime factors that are common to each of the original numbers. Include the highest variety of occurrences of each prime element that is typical to each initial number. Multiply these with each other to acquire the GCF.

You will check out that together numbers acquire larger the prime factorization technique may be much easier than directly factoring.

Example: find the GCF (18, 27)

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

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

The incidents of common prime components of 18 and also 27 are 3 and 3.

So the greatest common factor of 18 and 27 is 3 x 3 = 9.

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

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

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

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

### Euclid\"s Algorithm

What do you carry out if you desire to uncover the GCF of much more than 2 very huge numbers such together 182664, 154875 and also 137688? It\"s straightforward if you have actually a Factoring Calculator or a element Factorization Calculator or even the GCF calculator displayed above. However if you need to do the factorization by hand it will certainly be a lot of work.

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

provided two whole numbers, subtract the smaller sized number native the bigger number and note the result. Repeat the procedure subtracting the smaller number indigenous the an outcome until the result is smaller than the original tiny number. Usage the original small number as the brand-new larger number. Subtract the an outcome from step 2 native the new larger number. Repeat the procedure for every brand-new larger number and also smaller number till you with zero. As soon as you reach zero, go ago one calculation: the GCF is the number you uncovered just before the zero result.

For extr information see our Euclid\"s Algorithm Calculator.

Example: find the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

So, the greatest typical factor the 18 and also 27 is 9, the smallest an outcome we had prior to we reached 0.

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

Note that the GCF (x,y,z) = GCF (GCF (x,y),z). In various other words, the GCF that 3 or an ext numbers deserve to be uncovered by detect the GCF the 2 numbers and using the result along through the next number to find the GCF and also so on.

Let\"s get 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 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 the 20 and also 10 is 10.

Therefore, the greatest common factor that 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 of 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 137688 is 3.

Therefore, the greatest common factor that 182664, 154875 and 137688 is 3.

### References

<1> Zwillinger, D. (Ed.). CRC typical Mathematical Tables and also Formulae, 31st Edition. Brand-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.