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

You are watching: Gcf of 12 15 and 18  ## Calculator Use

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

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

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

Greatest typical factor (GCF) Greatest usual denominator (GCD) Highest usual factor (HCF) Greatest common 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 largest positive integer the divides evenly right into all numbers v zero remainder. For example, because that the collection of numbers 18, 30 and also 42 the GCF = 6.

## Greatest typical Factor that 0

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

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

For example, 5 × 0 = 0 so the 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 whole number k.

However, GCF(0, 0) is undefined.

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

There room several ways to discover the greatest typical factor of numbers. The most efficient technique you use relies on how countless numbers you have, how large they are and also what you will do with the result.

### Factoring

To find the GCF by factoring, list out all of the components of every number or discover them with a determinants Calculator. The totality number components are numbers that division evenly right into the number through zero remainder. Provided the perform of usual factors for each number, the GCF is the largest number typical to each list.

Example: find the GCF of 18 and also 27

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

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

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

The greatest typical factor the 18 and 27 is 9.

Example: uncover the GCF that 20, 50 and 120

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

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

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

The common factors the 20, 50 and also 120 room 1, 2, 5 and 10. (Include only the factors typical to all 3 numbers.)

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

### Prime Factorization

To discover the GCF by prime factorization, perform out every one of the prime factors of each number or discover them v a Prime determinants Calculator. Perform the prime determinants that are usual to every of the initial numbers. Include the highest number of occurrences of each prime variable that is common to each initial number. Main point these with each other to obtain the GCF.

You will see that together numbers acquire larger the element factorization method may be simpler than directly factoring.

Example: find the GCF (18, 27)

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

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

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

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

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

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

The element factorization that 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 occurrences of typical prime determinants of 20, 50 and also 120 room 2 and 5.

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

### Euclid"s Algorithm

What execute you do if you want to uncover the GCF of an ext than 2 very huge numbers such together 182664, 154875 and 137688? It"s straightforward if you have a Factoring Calculator or a element Factorization Calculator or even the GCF calculator displayed above. But if you should do the administrate by hand it will certainly be a many work.

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

given two entirety numbers, subtract the smaller sized number indigenous the bigger number and also note the result. Repeat the procedure subtracting the smaller number native the result until the result is smaller than the original small number. Usage the original little number as the new larger number. Subtract the result from step 2 indigenous the brand-new larger number. Repeat the procedure for every new larger number and smaller number until you reach zero. When you reach zero, go earlier one calculation: the GCF is the number you uncovered just before the zero result.

For additional information check out our Euclid"s Algorithm Calculator.

Example: uncover the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

So, the greatest typical factor the 18 and also 27 is 9, the smallest result we had before we reached 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 the 3 or much more numbers can be discovered by recognize the GCF of 2 numbers and also 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 typical factor that 120 and 50 is 10.

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

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

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

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

Example: find the GCF (182664, 154875, 137688) or GCF (GCF(182664, 154875), 137688)

First we find 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 of 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 common factor that 177 and 137688 is 3.

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

### References

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

See more: What Gauge Extension Cord For Microwave Into An Extension Cord?

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