for the worths 8, 12, 20Solution by Factorization:The factors of 8 are: 1, 2, 4, 8The determinants 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 greatest common factor of 4 and 12  ## Calculator Use

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

Enter 2 or more whole number separated by commas or spaces.

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

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

## What is the Greatest common Factor?

The greatest common factor (GCF or GCD or HCF) the a set of whole numbers is the largest positive integer that divides evenly into all numbers v zero remainder. For example, because that the set of number 18, 30 and also 42 the GCF = 6.

## Greatest usual Factor that 0

Any non zero entirety number times 0 equals 0 so it is true the every no zero entirety number is a element 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 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 find the Greatest common Factor (GCF)

There are several methods to uncover the greatest usual factor of numbers. The most efficient method you use relies on how many numbers friend have, how huge they are and what friend will do with the result.

### Factoring

To uncover the GCF through factoring, perform out all of the determinants of each number or uncover them through a components Calculator. The entirety number factors are number that division evenly into the number through zero remainder. Offered the perform of typical factors for each number, the GCF is the biggest number usual to each list.

Example: uncover the GCF that 18 and also 27

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

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

The usual factors the 18 and 27 are 1, 3 and 9.

The greatest common factor that 18 and 27 is 9.

Example: discover the GCF that 20, 50 and 120

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

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

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

The typical factors that 20, 50 and also 120 space 1, 2, 5 and also 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 uncover 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 determinants that are usual to each of the original numbers. Include the highest number of occurrences of each prime element that is usual to each original number. Main point these with each other to acquire the GCF.

You will view that together numbers gain larger the prime factorization technique may be easier than directly factoring.

Example: find the GCF (18, 27)

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

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

The cases of typical prime components of 18 and also 27 are 3 and also 3.

So the greatest usual factor of 18 and also 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 element 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 room 2 and 5.

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

### Euclid"s Algorithm

What do you do if you desire to discover the GCF of much more than two very huge numbers such as 182664, 154875 and 137688? It"s easy 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 administer by hand it will certainly be a most work.

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

given two whole numbers, subtract the smaller number from the bigger number and also note the result. Repeat the process subtracting the smaller sized number indigenous the result until the result is smaller sized than the original tiny number. Usage the original tiny number as the new larger number. Subtract the an outcome from step 2 native the brand-new larger number. Repeat the process for every brand-new larger number and also smaller number till you with zero. When you reach zero, go back 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: find 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 an outcome we had before we reached 0.

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

Note the the GCF (x,y,z) = GCF (GCF (x,y),z). In various other words, the GCF the 3 or an ext numbers have the right to be uncovered by finding the GCF of 2 numbers and also using the an outcome along v the following number to uncover the GCF and also 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 typical factor that 120 and also 50 is 10.

Now let"s discover the GCF that our 3rd value, 20, and our result, 10. GCF (20,10)

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

So, the greatest common factor that 20 and 10 is 10.

Therefore, the greatest common factor that 120, 50 and also 20 is 10.

Example: uncover 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 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 of 177 and 137688 is 3.

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

### References

<1> Zwillinger, D. (Ed.). CRC conventional Mathematical Tables and Formulae, 31st Edition. New York, NY: CRC Press, 2003 p. 101.

See more: What Is The Molarity Of 2 Mol Of Kl Dissolved In 1 L Water ?

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