**Greatest Common Factor (GCF) Calculator**

An on-line calculator to calculate the best not unusualplace issue GCF of integers.

**Definition of GCF**

The best not unusualplace issue (GCF) is the most important range this is issue to 2 or extra numbers. To locate the the GCF, we first specify the 2 numbers because they fabricated from high elements after which choose all of the elements which can be not unusualplace to each number and multiply them.

Example 1Find the GCF of forty and 60SolutionWe first specific 20 and 60 because the fabricated from high numbers forty = 2 × 2 × 2 × 560 = 2 × 2 × three × 5The not unusualplace elements are 2 × 2 and 5GCF of forty and 60 = 2 × 2 × 5 = 20

**Use of GCF to Reduce Fractions**

The GCF of the numerator and denominator of a given fraction can be used to lessen the fraction.

Example 2Reduce the fraction 18 / one hundred twentySolutionGCF of 18 and one hundred twenty12 = 2 × three × three one hundred twenty = 2 × 2 × 2 × three × 5GCF of 18 and one hundred twenty = 2 × three = 6We now lessen the given fraction 18 / one hundred twenty through dividing the numerator 18 and denominator one hundred twenty through the GCG of 18 and one hundred twenty located above.18 / one hundred twenty = 18÷6 / one hundred twenty÷6 = three / 20

**Use of GCF to Factor Algebraic Expressions**

Example threeFactor absolutely 32 x + 24 y + sixteen z.SolutionFind the GCF of the coefficient 32, 24 and sixteen.Express 32, 24 and sixteen as fabricated from high numbers32 = 2 × 2 × 2 × 2 × 224 = 2 × 2 × 2 × threesixteen = 2 × 2 × 2 × 2GCF of 32, 24 and sixteen = 2 × 2 × 2 = 8Since we’re factoring absolutely, we ought to take the GCF because the not unusualplace issue withinside the given expression. Hence32 x + 24 y + sixteen z = 8 (four x + three y + 2 z)

**Calculator Use**

Calculate GCF, GCD, and HCF of a fixed of or greater numbers and notice the paintings the usage of factorization.

Enter 2 or greater entire numbers separated with the aid of using commas or spaces.

The Greatest Common Factor Calculator answer additionally works as an answer for locating:

- Greatest not unusual place element (GCF)
- Greatest not unusual place denominator (GCD)
- Highest not unusual place element (HCF)
- Greatest not unusual place divisor (GCD)

**What is the Greatest Common Factor?**

The finest not unusual place element (GCF or GCD or HCF) of a fixed of entire numbers is the most important advantageous integer that divides frivolously into all numbers with 0 remainder. For example, for the set of numbers 18, 30, and forty-two the GCF = 6.

**Greatest Common Factor of zero**

Any non 0 entire quantity instances zero equals zero so it’s miles real that each non 0 entire quantity is an element of zero.

okay × zero = zero so, zero ÷ okay = zero for any entire quantity okay.

For example, five × zero = zero so it’s miles real that zero ÷ five = zero. In this example, five and zero are elements of zero.

GCF (five, zero) = five and greater normally GCF (okay, zero) = okay for any entire quantity okay.

However, GCF (zero, zero) is undefined.

**How to Find the Greatest Common Factor (GCF)?**

There are numerous methods to locate the finest not unusual place element of numbers. The maximum green approach you operate relies upon what number of numbers you have, how huge there, and what you’ll do with the end result.

**Factoring**

To locate the GCF with the aid of using factoring, listing out all the elements of every quantity, or locate them with a Factors Calculator. The entire quantity elements are numbers that divide frivolously into the quantity with 0 remainders. Given the listing of not unusual place elements for every quantity, the GCF is the most important quantity not un usual place to every listing.

**Example: Find the GCF of 18 and 27**

The elements of 18 are 1, 2, three, 6, 9, 18.

The elements of 27 are 1, three, 9, 27.

The not unusual place elements of 18 and 27 are 1, three, and 9.

The finest not unusual place element of 18 and 27 is 9.

**Example: Find the GCF of 20, 50, and one hundred twenty**

The elements of 20 are 1, 2, 4, five, 10, 20.

The elements of fifty are 1, 2, five, 10, 25, 50.

The elements of one hundred twenty are 1, 2, three, 4, five, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, one hundred twenty.

The not unusual place elements of 20, 50, and one hundred twenty are 1, 2, five, and 10. (Include most effective the elements not unusual place to all 3 numbers.)

The finest not unusual place element of 20, 50 and one hundred twenty is 10.

**Prime Factorization**

To locate the GCF with the aid of using high factorization, listing out all the high elements of every quantity or locate them with a Prime Factors Calculator. List the high elements which can be not unusual place to each of the authentic numbers. Include the best quantity of occurrences of every high element this is not an un usual place to every authentic quantity. Multiply those collectively to get the GCF.

You will see that as numbers get large the high factorization approach can be simpler than immediately factoring.

**Example: Find the GCF (18, 27)**

The high factorization of 18 is two x three x three = 18.

The high factorization of 27 is three x three x three = 27.

The occurrences of not un usual place high elements of 18 and 27 are three and three.

So the finest not un usual place element of 18 and 27 is three x three = 9.

**Example: Find the GCF (20, 50, one hundred twenty)**

The high factorization of 20 is two x 2 x five = 20.

The high factorization of fifty is two x five x five = 50.

The high factorization of one hundred twenty is two x 2 x 2 x three x five = one hundred twenty.

The occurrences of not un usual place high elements of 20, 50 and one hundred twenty are 2 and five.

So the finest not un usual place element of 20, 50 and one hundred twenty is two x five = 10.

**Euclid’s Algorithm**

What do you do in case you need to locate the GCF of greater than very huge numbers including 182664, 154875 and 137688? It’s clean when you have a Factoring Calculator or a Prime Factorization Calculator or maybe the GCF calculator proven above. But in case you want to do the factorization with the aid of using hand it’ll be a variety of paintings.

**How to Find the GCF Using Euclid’s Algorithm**

- Given entire numbers, subtract the smaller quantity from the bigger quantity and notice the end result.
- Repeat the system subtracting the smaller quantity from the end result till the end result is smaller than the authentic small quantity.
- Use the authentic small quantity as the brand new large quantity. Subtract the end result from Step 2 from the brand new large quantity.
- Repeat the system for each new large quantity and smaller quantity till you attain 0.
- When you attain 0, cross again one calculation: the GCF is the quantity you determined simply earlier than the 0 end result.

For extra data see our Euclid’s Algorithm Calculator.

**Example: Find the GCF (18, 27)**

27 – 18 = 9

18 – 9 – 9 = zero

So, the finest not un usual place element of 18 and 27 is 9, the smallest end result we had earlier than we reached zero.

**Example: Find the GCF (20, 50, one hundred twenty)**

Note that the GCF (x,y,z) = GCF (GCF (x,y),z). In different words, the GCF of three or greater numbers may be determined with the aid of using locating the GCF of two numbers and the usage of the end result together with the subsequent quantity to locate the GCF and so on.

Let’s get the GCF (one hundred twenty,50) first

one hundred twenty – 50 – 50 = one hundred twenty – (50 * 2) = 20

50 – 20 – 20 = 50 – (20 * 2) = 10

20 – 10 – 10 = 20 – (10 * 2) = zero

So, the finest not un usual place element of one hundred twenty and 50 is 10.

Now let’s locate the GCF of our 1/3 value, 20, and our end result, 10. GCF (20,10)

20 – 10 – 10 = 20 – (10 * 2) = zero

So, the finest not un usual place element of 20 and 10 is 10.

Therefore, the finest not un usual place element of one hundred twenty, 50 and 20 is 10.

**Example: Find the GCF (182664, 154875, 137688) or GCF (GCF(182664, 154875), 137688)**

First we discover the GCF (182664, 154875)

182664 – (154875 * 1) = 27789

154875 – (27789 * five) = 15930

27789 – (15930 * 1) = 11859

15930 – (11859 * 1) = 4071

11859 – (4071 * 2) = 3717

4071 – (3717 * 1) = 354

3717 – (354 * 10) = 177

354 – (177 * 2) = zero

So, the the finest not un usual place element 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) = three

15 – (three * five) = zero

So, the finest not un usual place element of 177 and 137688 is three.

Therefore, the finest not un usual place element of 182664, 154875 and 137688 is three.

### What is the Greatest Common Factor?

The best not unusualplace issue among numbers is the largestissue that each numbers are divisible via way of means of. Sometimes the bestnot unusualplace issue is likewise called the best not unusualplace divisor (gcd),or the best not unusualplace issue (hcf).

For example, locate the GCF of the 2 numbers 12 and sixteen:

The elements for 12 are 1, 2, 3, four, 6 and 12. These are elements of 12 because12 is divisible via way of means of all of those numbers.

The elements for sixteen are 1, 2, four, 8, sixteen.

The numbers (12 and sixteen) percentage not unusualplace elements (1, 2, four).The best of those is four and this is the best not unusualplace issue.

To use this Least Common Multiple Calculator (LCM Calculator), Enter a value in the first input (comma separated), select the method, and click on the **calculate button**.

Work with setup Gcf

Input Data :Data set = five, 20, 40, 80, one hundredTotal range of elements = fiveObjective :Find the GCF of given integers?Solution :Find top elements for every inputfive = five20 = 2 x 2 x five40 = 2 x 2 x 2 x five80 = 2 x 2 x 2 x 2 x fiveone hundred = 2 x 2 x five x fiveCommon element for five, 20, 40, 80, one hundred is five

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