for the worths 8, 12, 20Solution through Factorization:The factors of 8 are: 1, 2, 4, 8The factors of 12 are: 1, 2, 3, 4, 6, 12The components of 20 are: 1, 2, 4, 5, 10, 20Then the greatest usual factor is 4.

You are watching: What is the gcf of 30  ## Calculator Use

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

Enter 2 or an ext whole numbers separated through commas or spaces.

The Greatest usual Factor Calculator solution likewise works together a solution for finding:

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

## What is the Greatest usual Factor?

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

## Greatest common Factor the 0

Any no zero whole number times 0 amounts to 0 so the is true that every non zero whole number is a factor of 0.

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

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

There are several means to discover the greatest typical factor that numbers. The many efficient method you use depends on how many numbers you have, how big they are and also what friend will do with the result.

### Factoring

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

Example: uncover the GCF of 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 common factors that 18 and also 27 room 1, 3 and 9.

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

Example: discover the GCF that 20, 50 and 120

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

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

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

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

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

### Prime Factorization

To discover the GCF by prime factorization, perform out all of the prime factors of every number or uncover them v a Prime components Calculator. Perform the prime factors that are typical to every of the original numbers. Encompass the highest number of occurrences of every prime factor that is usual to each initial number. Multiply these with each other to obtain the GCF.

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

Example: discover the GCF (18, 27)

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

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

The occurrences of typical prime components of 18 and also 27 space 3 and 3.

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

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

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

The prime 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 determinants of 20, 50 and 120 space 2 and also 5.

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

### Euclid"s Algorithm

What carry out you execute if you want to discover the GCF of an ext than two very huge numbers such together 182664, 154875 and also 137688? It"s straightforward if you have actually a Factoring Calculator or a prime Factorization Calculator or also the GCF calculator shown above. However if you must do the factorization by hand it will certainly be a many work.

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

provided two whole numbers, subtract the smaller number from the bigger number and also note the result. Repeat the process subtracting the smaller sized number from the result until the result is smaller sized than the original tiny number. Usage the original little number together the brand-new larger number. Subtract the result from action 2 indigenous the new larger number. Repeat the process for every new larger number and smaller number till you with zero. Once you reach zero, go ago one calculation: the GCF is the number you discovered just prior to the zero result.

For added information view our Euclid"s Algorithm Calculator.

Example: discover the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

So, the greatest common factor the 18 and 27 is 9, the smallest result we had before we reached 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 that 3 or much more numbers can be uncovered by detect the GCF the 2 numbers and also using the an outcome along through the next number to discover the GCF and also so on.

Let"s gain 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 typical factor the 120 and 50 is 10.

Now let"s find the GCF the 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 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 common 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 137688 is 3.

Therefore, the greatest usual factor that 182664, 154875 and 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 usual Divisor." indigenous MathWorld--A Wolfram net Resource.