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 factors of 20 are: 1, 2, 4, 5, 10, 20Then the biggest common aspect is 4.

You are watching: Gcf of 16 20 and 24  ## Calculator Use

Calculate GCF, GCD and also HCF of a set of 2 or more numbers and also check out the job-related making use of factorization.

Go into 2 or even more whole numbers separated by commas or spaces.

The Greatest Common Factor Calculator solution also works as a solution for finding:

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

## What is the Greatest Typical Factor?

The best widespread element (GCF or GCD or HCF) of a set of entirety numbers is the biggest positive integer that divides evenly right into all numbers through zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.

## Greatest Common Factor of 0

Any non zero whole number times 0 equates to 0 so it is true that eexceptionally non zero whole number is a variable of 0.

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

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

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

However before, GCF(0, 0) is undefined.

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

There are several ways to uncover the biggest widespread element of numbers. The most efficient method you usage depends on just how many numbers you have actually, exactly how big they are and what you will execute with the outcome.

### Factoring

To uncover the GCF by factoring, list out every one of the determinants of each number or uncover them through a Factors Calculator. The totality number determinants are numbers that divide evenly right into the number with zero remainder. Given the list of common factors for each number, the GCF is the biggest number prevalent to each list.

Example: Find the GCF of 18 and 27

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

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

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

The greatest prevalent variable of 18 and 27 is 9.

Example: Find the GCF of 20, 50 and 120

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

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

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

The common determinants of 20, 50 and 120 are 1, 2, 5 and 10. (Include just the determinants common to all 3 numbers.)

The best prevalent variable of 20, 50 and 120 is 10.

### Prime Factorization

To uncover the GCF by prime factorization, list out every one of the prime components of each number or find them via a Prime Factors Calculator. List the prime factors that are common to each of the original numbers. Include the highest number of events of each prime variable that is common to each original number. Multiply these together to get the GCF.

You will check out that as numbers get larger the prime factorization method may be much easier than straight 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 occurrences of common prime components of 18 and 27 are 3 and also 3.

So the greatest prevalent factor of 18 and also 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 occurrences of common prime determinants of 20, 50 and 120 are 2 and also 5.

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

### Euclid"s Algorithm

What execute you perform if you want to find the GCF of more than 2 incredibly 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 also the GCF calculator presented above. But if you have to perform the factorization by hand also it will be the majority of job-related.

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

Given 2 whole numbers, subtract the smaller number from the bigger number and note the outcome. Repeat the process subtracting the smaller number from the result until the outcome is smaller than the original little number. Use the original small number as the brand-new larger number. Subtract the result from Step 2 from the new larger number. Repeat the process for eincredibly brand-new larger number and smaller number till you reach zero. When you reach zero, go back one calculation: the GCF is the number you found just before the zero outcome.

For extra indevelopment view our Euclid"s Algorithm Calculator.

Example: Find the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

So, the best widespread aspect of 18 and 27 is 9, the smallest result we had actually before we reached 0.

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

Keep in mind 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 making use of the result along with the next number to discover 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 biggest common aspect of 120 and also 50 is 10.

Now let"s uncover the GCF of our third worth, 20, and our outcome, 10. GCF (20,10)

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

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

Thus, the greatest prevalent factor of 120, 50 and 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 prevalent 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 best widespread aspect of 177 and also 137688 is 3.

Therefore, the best widespread aspect of 182664, 154875 and also 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 Typical Divisor." From MathWorld--A Wolfram Web Reresource.