for the values 8, 12, 20Equipment by Factorization:The determinants of 8 are: 1, 2, 4, 8The components of 12 are: 1, 2, 3, 4, 6, 12The determinants of 20 are: 1, 2, 4, 5, 10, 20Then the best common aspect is 4.

You are watching: Greatest common factor of 15 and 21  ## Calculator Use

Calculate GCF, GCD and HCF of a collection of 2 or more numbers and also view the occupational utilizing factorization.

Get in 2 or even more whole numbers separated by commas or spaces.

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

Greatest prevalent factor (GCF) Greatest common denominator (GCD) Highest common variable (HCF) Greatest prevalent divisor (GCD)

## What is the Greatest Usual Factor?

The biggest common factor (GCF or GCD or HCF) of a set of totality numbers is the biggest positive integer that divides evenly right into all numbers with zero remainder. For example, for the set of numbers 18, 30 and also 42 the GCF = 6.

## Greatest Usual Factor of 0

Any non zero totality number times 0 equals 0 so it is true that every non zero totality number is a variable of 0.

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

For example, 5 × 0 = 0 so it is true that 0 ÷ 5 = 0. In this instance, 5 and also 0 are components of 0.

GCF(5,0) = 5 and also even more mostly GCF(k,0) = k for any entirety number k.

However, GCF(0, 0) is uncharacterized.

## How to Find the Greatest Usual Factor (GCF)

Tright here are several means to uncover the greatest widespread element of numbers. The most efficient approach you usage depends on exactly how many kind of numbers you have, how big they are and also what you will certainly carry out with the outcome.

### Factoring

To discover the GCF by factoring, list out all of the components of each number or discover them through a Factors Calculator. The entirety number factors are numbers that divide evenly into the number through zero remainder. Given the list of widespread factors for each number, the GCF is the biggest number common to each list.

Example: Find the GCF of 18 and 27

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

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

The prevalent components of 18 and also 27 are 1, 3 and also 9.

The best prevalent variable of 18 and 27 is 9.

Example: Find the GCF of 20, 50 and 120

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

The determinants 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 prevalent components of 20, 50 and also 120 are 1, 2, 5 and also 10. (Include only the determinants widespread to all 3 numbers.)

The greatest widespread variable of 20, 50 and also 120 is 10.

### Prime Factorization

To uncover the GCF by prime factorization, list out all of the prime components of each number or discover them through a Prime Factors Calculator. List the prime components that are widespread to each of the original numbers. Include the highest possible number of cases of each prime variable that is prevalent to each original number. Multiply these together to acquire the GCF.

You will watch that as numbers obtain bigger the prime factorization strategy may be easier than right factoring.

Example: Find the GCF (18, 27)

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

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

The incidents of prevalent prime factors of 18 and 27 are 3 and 3.

So the biggest prevalent element of 18 and 27 is 3 x 3 = 9.

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

The prime 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 determinants of 20, 50 and 120 are 2 and 5.

So the biggest prevalent aspect of 20, 50 and also 120 is 2 x 5 = 10.

### Euclid"s Algorithm

What execute you perform if you want to uncover the GCF of more than 2 extremely big numbers such as 182664, 154875 and also 137688? It"s simple if you have actually a Factoring Calculator or a Prime Factorization Calculator or even the GCF calculator displayed over. But if you must carry out the factorization by hand also it will be most occupational.

## How to Find the GCF Using Euclid"s Algorithm

Given two entirety numbers, subtract the smaller sized number from the larger number and also note the result. Repeat the process subtracting the smaller sized number from the outcome until the outcome is smaller sized than the original little number. Use the original tiny number as the brand-new bigger number. Subtract the outcome from Step 2 from the brand-new larger number. Repeat the procedure for eexceptionally brand-new bigger number and also smaller number until you reach zero. When you reach zero, go ago one calculation: the GCF is the number you uncovered just prior to the zero result.

For additional indevelopment see our Euclid"s Algorithm Calculator.

Example: Find the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

So, the biggest common variable of 18 and 27 is 9, the smallest outcome we had actually before we reached 0.

Example: Find 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 even more numbers deserve to be found by finding the GCF of 2 numbers and also using the result in addition to the next number to discover the GCF and 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 best common element of 120 and also 50 is 10.

Now let"s find the GCF of our 3rd worth, 20, and also our result, 10. GCF (20,10)

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

So, the biggest widespread element of 20 and 10 is 10.

Because of this, the best widespread variable of 120, 50 and also 20 is 10.

Example: Find 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 best widespread element of 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 biggest widespread variable of 177 and 137688 is 3.

As such, the biggest common factor of 182664, 154875 and 137688 is 3.

### References

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

See more: What Is The Diameter Of A 60 Inch Round Table ? 60 Inch Round

<2> Weisstein, Eric W. "Greatest Common Divisor." From MathWorld--A Wolfram Internet Resource.