for the values 8, 12, 20Solution by Factorization:The components of 8 are: 1, 2, 4, 8The components 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 gcf of 30 and 42  ## Calculator Use

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

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

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

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

## What is the Greatest common Factor?

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

## Greatest common Factor the 0

Any non zero totality number times 0 equates to 0 so it is true that every non zero totality number is a factor of 0.

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

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

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

However, GCF(0, 0) is undefined.

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

There are several methods to discover the greatest typical factor that numbers. The most efficient method you use counts on how plenty of numbers friend have, how large they are and also what friend will perform with the result.

### Factoring

To find the GCF by factoring, perform out all of the factors of every number or uncover them v a factors Calculator. The entirety number determinants are numbers that divide evenly right 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: discover the GCF the 18 and also 27

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

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

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

The greatest typical factor that 18 and 27 is 9.

Example: find the GCF that 20, 50 and 120

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

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

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

### Prime Factorization

To find the GCF by element factorization, list out every one of the prime factors of every number or discover them v a Prime determinants Calculator. List the prime factors that are typical to each of the initial numbers. Encompass the highest variety of occurrences of each prime factor that is common to each initial number. Main point these with each other to get the GCF.

You will watch that together numbers acquire larger the element factorization technique may be easier than directly factoring.

Example: find the GCF (18, 27)

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

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

The events of common prime components of 18 and also 27 room 3 and also 3.

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

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

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

The prime factorization of 50 is 2 x 5 x 5 = 50.

The element factorization that 120 is 2 x 2 x 2 x 3 x 5 = 120.

The events of common prime determinants of 20, 50 and also 120 room 2 and also 5.

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

### Euclid\"s Algorithm

What perform you execute if you want to uncover the GCF of an ext than 2 very big numbers such as 182664, 154875 and 137688? It\"s basic if you have a Factoring Calculator or a element Factorization Calculator or also the GCF calculator presented above. But if you need to do the administer by hand it will be a many work.

## How to find the GCF utilizing Euclid\"s Algorithm

provided two whole numbers, subtract the smaller sized number native the larger number and also note the result. Repeat the process subtracting the smaller number native the result until the result is smaller sized than the original tiny number. Usage the original little number together the new larger number. Subtract the an outcome from step 2 from the new larger number. Repeat the process for every new larger number and smaller number till you with zero. When you with zero, go earlier one calculation: the GCF is the number you discovered just prior to the zero result.

For additional 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 that 18 and 27 is 9, the smallest an outcome we had prior to we got to 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 more numbers can be discovered by finding the GCF that 2 numbers and using the an outcome along with the following number to discover 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 common factor of 120 and also 50 is 10.

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

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

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

Therefore, the greatest common factor that 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 usual factor that 182664 and also 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 usual factor the 177 and 137688 is 3.

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

### References

<1> Zwillinger, D. (Ed.). CRC standard 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.