for the values 8, 12, 20Solution through 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 16 and 30  ## Calculator Use

Calculate GCF, GCD and also HCF the a collection of two or an ext numbers and also see the job-related using factorization.

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

The Greatest typical Factor Calculator solution likewise works as a systems for finding:

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

## What is the Greatest common Factor?

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

## Greatest common Factor the 0

Any non zero totality number time 0 equates to 0 so the is true the every no zero entirety 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 the 0 ÷ 5 = 0. In this example, 5 and 0 are components 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 uncover the Greatest usual Factor (GCF)

There are several means to uncover the greatest typical factor that numbers. The many efficient an approach you use counts on how countless numbers girlfriend have, how large they are and also what girlfriend will perform with the result.

### Factoring

To discover the GCF by factoring, perform out all of the determinants of each number or uncover them through a components Calculator. The whole number components are number that divide evenly into the number through zero remainder. Offered the list of usual factors because that each number, the GCF is the largest number typical to every list.

Example: uncover the GCF that 18 and 27

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

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

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

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

Example: discover the GCF of 20, 50 and 120

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

The components of 50 space 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 common factors that 20, 50 and also 120 room 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 find the GCF by prime factorization, perform out all of the prime determinants of every number or uncover them v a Prime components Calculator. Perform the prime factors that are common to every of the initial numbers. Encompass the highest number of occurrences of every prime factor that is typical to each original number. Multiply these together to acquire the GCF.

You will see that as numbers get larger the element factorization an approach 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 element factorization the 27 is 3 x 3 x 3 = 27.

The events of typical prime determinants of 18 and 27 are 3 and 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 prime factorization of 50 is 2 x 5 x 5 = 50.

The prime factorization of 120 is 2 x 2 x 2 x 3 x 5 = 120.

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

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

### Euclid"s Algorithm

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

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

given two entirety numbers, subtract the smaller sized number from the larger number and also note the result. Repeat the procedure subtracting the smaller sized number from the result until the result is smaller sized than the original tiny number. Use the original small number together the new larger number. Subtract the an outcome from action 2 indigenous the new larger number. Repeat the process for every new larger number and also smaller number until 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 check out our Euclid"s Algorithm Calculator.

Example: discover 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 before we reached 0.

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

Note the the GCF (x,y,z) = GCF (GCF (x,y),z). In various other words, the GCF of 3 or much more numbers can be discovered by finding the GCF that 2 numbers and using the an outcome along with 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 the 120 and 50 is 10.

Now let"s find the GCF the our third value, 20, and our result, 10. GCF (20,10)

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

So, the greatest usual factor the 20 and also 10 is 10.

Therefore, the greatest usual 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 typical 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 usual factor the 177 and also 137688 is 3.

Therefore, the greatest common factor of 182664, 154875 and 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 internet Resource.