**Math Calculators** ▶ GCF Calculator (Greatest Common Factor) HCF,GCD

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An online gcf calculator helps to find greatest common factor of two or more integers by using different gcf methods. Even this gcd calculator can helps to find the step-by-step calculation of greatest common divisor for the given integers.

The context provides with the ultimate guide on how to find gcf using different methods (manually) and with gcf finder, and correlated terms of GCD.

In fact, basics are the first, so we decided to begin with GCF definition!

Read on!

In mathematics, the GCF of two or more integers is said to be as the largest positive integer, which divides each of the integers with zero remainder. For example, the greatest common factor of 8 and 10 is 2, because 2 divides both 8 and 10, and no larger number this property.

Well, there are different other names for the GCF concept included:

- Great Common Measure
- Greatest Common Divisor or Greatest Common Denominator (GCD)
- Highest Common Factor (HCF)
- Greatest Common Multiple
- Highest Common Divisor (HCD)

So, simply add the two or more integers into an online gcf calculator, and lets it do the calculations instantly.

When it comes to quotient and remainder calculations, you can try this free quotient and remainder calculator that helps to divide two numbers to find the quotient with remainder instantly. Also, use a simple, but accurate mod calculator that allows you to find the result of any modulus operation between integer numbers.

Now, we discuss the four different gcf calculation methods with their manual calculations. This online gcf finder uses the following formulas to find the greatest or highest common factor of the given data set.

All you need to list all the factors of given integers. Then, list the common factors of all the integers, the GCF is the greatest number in the list.

Here we have an example to clear the concept of calculation by listing the factors.

**For Example:**

What is the greatest common factor of 6,10 and 12?

**Solution:**

Factors of 6 = 1,2,3,6

Factors of 10 = 1,2,5,10

Factors of 12 = 1,2,3,4,6,12

List of all the common factors in each of integer = 1,2

Here, the greatest number which is on the list is 2.

So, the GCF of 6,10,12 is 2.

You can enter the same integers into the online gcd calculator to verify your solved results of gcd.

Another method to find the gcf of the given data set is the prime factorization method, even our online gcf calculator helps to solve the greatest common divisor according to this method. To find the gcf by prime factorization method manually, simply write all the prime factors of each of the numbers. You can also use our online prime factorization calculator that makes the prime factors of any number and tells you whether a number is prime or not. Then, list the numbers that are common to each integer. Multiply these common factors to get the highest common factor(HCF) of integers. Let’s try an example of this method:

**For Example:**

What is the Greatest Common Divisor of 15,40 and 90?

**Solution:**

Prime factors of 15 = 1,3,5,15

Prime factors of 40 = 1,2,4,5,8,10,20,40

Prime factors of 90 = 1,2,3,5,6,9,10,15,18,30,45,90

Common factors = 1,5

HCF = 1 × 5

So, the GCF of 15,40,90 is 5.

Another method to find the gcd is by using the Euclidean algorithm. This method is more efficient than the prime factorization method. This gcf calculator uses the following points to determine the greatest common divisor according to this method:

- From the given two numbers, subtract the smaller number from the larger number.
- Then subtract the smaller number from the result.
- Repeat the process until the result is smaller than the original smaller number.
- Consider the small number as a large number, subtract the result of the previous step from the new large number.
- Repeat the process, until you reach zero.
- When the result is zero, the gcf of the numbers is the number you found before the zero result.

Let’s try an example of this method:

**For example:**

What is a greatest common factor of 22 and 33?

**Solution:**

33-22 = 11

22-11 = 11

11-11 = 0

So, the gcf of 22 and 33 is 11.

It doesn’t matter whether you have two or more integers, simply add them into an online gcd calculator that find the greatest common divisor for the given values.

**Example:**

Find the gcd of 15,45 and 115?

**Solution:**

As,

gcf (a, b, c) = gcf {gcf (a, b), c}

So,

Let’s we compute the gcf of 115 and 45,

115-45 = 70

45-70 = 25

45-25 = 15

25-15 = 10

15-10 = 5

10-5 = 5

5-5 = 0

So the gcf of 115 and 45 is 5.

Now, find the gcf of third value 15 and the result 5.

15-5 = 10

5-10 = 5

5-5 = 0

So, the greatest common divisor of 15 and 5 is 5.

Therefore,

The gcf of 15,45 and 115 is 5.

The last method to find the gcf of the integers used by this gcf calculator is by Binary Stein’s Algorithm. In this Binary Stein’s Algorithm or Binary GCD Algorithm, you simply use the comparison, subtraction and divide by 2. This method to find greatest common divisor comprises of:

- Sort all the numbers/integers in Ascending order.
- Suppose the initial GCF is 1.
- Divide all the even numbers with 2.
- Sort the values in ascending order and remove if any duplication occurs.
- Subtract the first number from the remaining numbers and divide by 2.
- Repeat these steps until you obtain a single value.

Let’s have an example to clarify the concept:

**For example:**

Find the gcf of 45,15 and 115?

**Solution:**

**Step 1:**

Sort numbers in ascending order:

15,45,115

**Step 2:**

Initial GCF is 1.

**Step 3:**

As there is no even and duplicate value, so it is as 15,45,115

**Step 4:**

Now,

(45-15)/2 = 15

(115-15)/2 = 50

So,15,15,50

**Step 5:**

Now again, divide the even value with 2.

So,15,15,25

**Step 6:**

Sort in ascending order and remove duplicate terms.

15,25

**Step 7:**

Subtract 25 from 15 and divided by 2.

(25-15)/2 = 5

So,

15,5

**Step 8:**

Now, again divide the even value with 2 and remove any duplicate value.

So, 5,15

**Step 9:**

Subtract 5 from 15 and divided by 2.

(15-5)/2 = 5

So,

5,5

**Step 10:**

Sort the value in ascending order and remove duplicate values.

So,

5

**Step 11:**

As there is only one term left, multiply it with your initial gcf:

5*1 = 5

Therefore 5 is the greatest or highest common factor of 15,45 and 115.

No doubt, finding gcd step-by-step is a complicated task, but thanks to the free online gcf calculator that find Gcf quickly and precisely.

The different properties are:

- If the ratio between two numbers (a, b) is an integer, then gcf (a, b) = b.
- The gcf of a number with 0 is always 0 i; e gcf(a,0) = 0.
- The gcf of a number with 1 is always 1 i; e gcf(a,1) = 1.
- If the numbers are coprime, then gcf will be 1.
- All the common factors of numbers are also divisors of the gcf of the number.
- For any integer z,

gcf (z*a, z*b) = z*gcf (a, b)

- For any integer z,

gcf (z/a, z/b) = gcf (a, b)/z

- gcf (a, b) *lcm (a, b) =a*b.

Well, simply use this best LCM calculator online to find the least common multiple (lcm) of the two to n numbers step-by-step corresponding to different LCM calculation methods.

The online HCF calculator lets you find the greatest or highest common factor according to the given methods:

- None (Simple Method)
- Listing Factors method.
- Prime Factorization method.
- Euclidean Algorithm.
- Binary Stein’s Algorithm

Now, let’s find out the steps that you have to follow while using this free online gcf finder:

Swipe on!

**Inputs:**

- First of all, you need to enter the two or more integers for which you want to find the greatest common factor (GCF)
- Then, you can select one gcf calculation method that we mentioned above
- Hit Calculate button

**Outputs:**

This greatest common divisor calculator will find the following:

- The Greatest Common Factor (GCF) of the given integers according to the selected method.
- Complete step-by-step calculations for the selected method.

An industry has 500 employees, if 280 are males then find the greatest number of groups that can be made if each group has an equal number of boys and each group has the same number of females.

In this condition, it is very difficult to answer. So, the GCF is helpful to determine the answer. Also, you can use our free greatest common factor calculator to solve the greatest common divisor-related mathematical problems.

As the greatest number that exactly divides the numbers is the greatest common factor. So, 6 is the largest number which exactly divides 12 and 18. Therefore 6 is the gcf of 12 and 18. Furthermore, you can enter the integers of your choice into online gcf calculator to find the greatest common measure instantly.

The prime factors of 12 = 2,2,3

The prime factors of 16 = 2,2,2,2

Common factors = 2*2

So, the hcf of 12 and 16 is 4.

We can calculate the hcf of 12 and 4 by listing factors method:

Factors of 12 = 1,2,3,4,6,12

Factors of 4 = 1,2,4

List of all the common factors = 1,2,4

The greatest number in the common factors is 4. So, the Highest common factor of 12 and 4 is 4.

We can find the GCF of 18 and 24 by prime factorization method as:

The prime factors of 18 = 2,3,3

The prime factors of 24 = 2,2,2,3

Common factors = 2*3

So, the gcf of 18 and 24 is 6.

Prime factors of 16 = 2,2,2,2

Prime factors of 24 = 2,2,2,3

Prime factors of 36 = 2,2,3,3

The common prime factors = 2*2

So the hcf of 16,24 and 36 is 4.

You can find the Greatest Common Divisor (GCD) of two numbers in excel, by using the GCD function. The syntax of GCD function in excel is as:

=GCD (number1, number2)

The Greatest common factor is helpful in real-life problems and in different applications of mathematics like to determine the common factors of polynomials. However, the online gcf calculator by calculator-online is specifically developed to find the tedious greatest common divisor computations.

From the source of Wikipedia: (GCD) or (GCF): Applications, Overview, Calculations & more!

From the source of sciencing: Two Common Methods – Simplify Factors With Steps (By Lee Johnson)

From the authorized source of effortlessmath: A simple step-by-step guide to find the (GCF)

The khanacademy provides with: GCF explained (Explore Now)

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