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

You are watching: What is the greatest common factor of 30 and 42  ## Calculator Use

Calculate GCF, GCD and HCF that a collection of 2 or more numbers and also see the job-related using factorization.

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

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

Greatest common factor (GCF) Greatest usual 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) the a collection of totality numbers is the biggest positive integer the divides evenly into all numbers with zero remainder. Because that example, because that the set of number 18, 30 and 42 the GCF = 6.

## Greatest usual Factor that 0

Any no zero whole number times 0 equates to 0 so the is true that every non zero entirety 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 it is true that 0 ÷ 5 = 0. In this example, 5 and also 0 are factors of 0.

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

However, GCF(0, 0) is undefined.

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

There room several ways to find the greatest usual factor that numbers. The most efficient technique you use counts on how numerous numbers you have, how large they are and also what girlfriend will carry out with the result.

### Factoring

To discover the GCF through factoring, list out every one of the factors of every number or uncover them through a determinants Calculator. The entirety number determinants are number that divide evenly right into the number with zero remainder. Provided the perform of typical factors because that each number, the GCF is the largest number usual to every list.

Example: uncover the GCF of 18 and also 27

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

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

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

The greatest common factor the 18 and 27 is 9.

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

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

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

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

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

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

### Prime Factorization

To find the GCF by prime factorization, list out every one of the prime components of every number or discover them through a Prime factors Calculator. List the prime determinants that are common to every of the original numbers. Incorporate the highest variety of occurrences of every prime variable that is common to each original number. Main point these with each other to get the GCF.

You will see that together numbers obtain larger the prime factorization method may be much easier than right factoring.

Example: find the GCF (18, 27)

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

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

The cases of typical prime components of 18 and 27 space 3 and 3.

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

Example: discover 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 element factorization of 120 is 2 x 2 x 2 x 3 x 5 = 120.

The events of common prime factors of 20, 50 and also 120 space 2 and also 5.

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

### Euclid"s Algorithm

What carry out you do if you want to uncover the GCF of more than 2 very huge numbers such together 182664, 154875 and also 137688? It"s basic if you have a Factoring Calculator or a element Factorization Calculator or even the GCF calculator shown above. But if you have to do the factorization by hand it will certainly be a many work.

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

given two totality numbers, subtract the smaller sized number from the larger number and note the result. Repeat the process subtracting the smaller number indigenous the an outcome until the an outcome is smaller than the original small number. Use the original little number together the brand-new larger number. Subtract the an outcome from action 2 from 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 found just prior to the zero result.

For extr information watch our Euclid"s Algorithm Calculator.

Example: discover the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

So, the greatest common factor that 18 and also 27 is 9, the smallest result we had before we got to 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 an ext numbers have the right to be found by detect the GCF of 2 numbers and also using the result along through the following number to find the GCF and 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 common factor that 120 and also 50 is 10.

Now let"s find the GCF the 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 typical 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 common factor that 182664 and 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 typical factor that 177 and also 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 also Formulae, 31st Edition. Brand-new York, NY: CRC Press, 2003 p. 101.

See more: What Is The Reciprocal Of 6/5 ? What Is The Reciprocal Of 6/5

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