for the worths 8, 12, 20Solution by Factorization:The components 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 typical factor is 4.

You are watching: Find the gcf 12 and 45  ## Calculator Use

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

Enter 2 or more whole numbers separated through commas or spaces.

The Greatest typical Factor Calculator solution additionally works together a systems for finding:

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

## What is the Greatest usual Factor?

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

## Greatest usual Factor of 0

Any no zero whole number time 0 amounts to 0 so it is true the every no zero whole number is a factor of 0.

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

For example, 5 × 0 = 0 so that is true the 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 type of whole number k.

However, GCF(0, 0) is undefined.

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

There room several methods to uncover the greatest common factor of numbers. The most efficient method you use relies on how numerous numbers friend have, how big they are and also what you will carry out with the result.

### Factoring

To discover the GCF through factoring, perform out every one of the factors of each number or uncover them with a components Calculator. The whole number components are numbers that division evenly right into the number through zero remainder. Given the perform of usual factors for each number, the GCF is the biggest number common to each list.

Example: discover the GCF that 18 and 27

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

The determinants of 27 are 1, 3, 9, 27.

The typical factors that 18 and also 27 are 1, 3 and also 9.

The greatest typical factor that 18 and 27 is 9.

Example: find the GCF that 20, 50 and 120

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

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

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

### Prime Factorization

To find the GCF by prime factorization, perform out every one of the prime factors of each number or uncover them through a Prime determinants Calculator. Perform the prime factors that are common to each of the original numbers. Include the highest variety of occurrences of each prime variable that is common to each initial number. Main point these together to acquire the GCF.

You will view that together numbers get larger the element factorization technique may be much easier than directly factoring.

Example: find the GCF (18, 27)

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

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

The events of usual prime determinants of 18 and 27 space 3 and also 3.

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

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

The prime factorization the 20 is 2 x 2 x 5 = 20.

The element factorization the 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 occurrences of usual prime determinants of 20, 50 and 120 are 2 and also 5.

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

### Euclid"s Algorithm

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

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

offered two totality numbers, subtract the smaller sized number indigenous the bigger number and note the result. Repeat the process subtracting the smaller sized number native the an outcome until the an outcome is smaller sized than the original little number. Usage the original little number together the brand-new larger number. Subtract the result from step 2 indigenous the brand-new larger number. Repeat the procedure for every brand-new larger number and also smaller number till you reach zero. When you reach zero, go earlier one calculation: the GCF is the number you discovered just before the zero result.

For extr information see our Euclid"s Algorithm Calculator.

Example: discover the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

So, the greatest usual factor that 18 and 27 is 9, the smallest result we had prior to 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 that 3 or much more numbers have the right to be uncovered by recognize the GCF of 2 numbers and using the an outcome along v the following number to uncover the GCF and so on.

Let"s acquire 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 also 50 is 10.

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

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

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

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

Example: discover 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 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 that 177 and also 137688 is 3.

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

### References

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

See more: Does Ham Go Bad? How To Tell If Ham Is Spoiled How To Know When Ham Has Gone Bad

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