for the worths 8, 12, 20Equipment by Factorization:The components 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 best prevalent element is 4.

You are watching: What is the gcf of 24,30 and 42  ## Calculator Use

Calculate GCF, GCD and also HCF of a set of two or more numbers and check out the work-related using factorization.

Enter 2 or more entirety numbers separated by commas or spaces.

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

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

## What is the Greatest Common Factor?

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

## Greatest Typical Factor of 0

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

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

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

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

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

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

Tbelow are a number of ways to uncover the biggest prevalent element of numbers. The the majority of effective approach you usage relies on exactly how many type of numbers you have actually, just how huge they are and what you will certainly carry out via the outcome.

### Factoring

To uncover the GCF by factoring, list out every one of the components of each number or find them with a Factors Calculator. The whole number components are numbers that divide evenly into the number via zero remainder. Given the list of widespread determinants for each number, the GCF is the biggest number prevalent to each list.

Example: Find the GCF of 18 and also 27

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

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

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

The greatest common variable of 18 and 27 is 9.

Example: Find the GCF of 20, 50 and also 120

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

The best common aspect of 20, 50 and 120 is 10.

### Prime Factorization

To discover the GCF by prime factorization, list out all of the prime components of each number or find them through a Prime Factors Calculator. List the prime factors that are widespread to each of the original numbers. Include the highest possible number of occurrences of each prime aspect that is widespread to each original number. Multiply these together to gain the GCF.

You will check out that as numbers acquire bigger the prime factorization approach may be simpler 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 determinants of 18 and 27 are 3 and also 3.

So the greatest widespread 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 incidents of common prime determinants of 20, 50 and 120 are 2 and 5.

So the biggest common variable of 20, 50 and 120 is 2 x 5 = 10.

### Euclid"s Algorithm

What do you do if you want to discover the GCF of more than two very big numbers such as 182664, 154875 and also 137688? It"s basic if you have a Factoring Calculator or a Prime Factorization Calculator or even the GCF calculator presented above. But if you need to execute the factorization by hand it will be many occupational.

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

Given 2 entirety numbers, subtract the smaller sized number from the bigger number and note the outcome. Repeat the procedure subtracting the smaller number from the result till the result is smaller sized than the original tiny number. Use the original little number as the new larger number. Subtract the outcome from Step 2 from the new larger number. Repeat the procedure for eextremely new bigger number and smaller number until you reach zero. When you reach zero, go earlier one calculation: the GCF is the number you uncovered simply before the zero outcome.

For extra indevelopment watch our Euclid"s Algorithm Calculator.

Example: Find the GCF (18, 27)

27 - 18 = 9

18 - 9 - 9 = 0

So, the greatest common factor of 18 and 27 is 9, the smallest outcome we had prior to 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 various other words, the GCF of 3 or more numbers have the right to be discovered by finding the GCF of 2 numbers and making use of the outcome together with the following number to discover the GCF and 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 biggest prevalent element of 120 and 50 is 10.

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

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

So, the best prevalent aspect of 20 and also 10 is 10.

As such, the best prevalent element 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 prevalent variable of 182664 and 154875 is 177.

Now we find 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 common factor of 177 and 137688 is 3.

Thus, the biggest prevalent factor of 182664, 154875 and 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.

See more: Which One Of The Following Sentences Is Correctly Punctuated

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