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

An online gcf calculator helps to calculate greatest common factor (GCF) , GCD, and HCF of a set of two or n numbers according to different gcf methods. This HCF calculator allows you to determine the step-by-step calculations for the highest common factor.

Give a complete read to know about how to find the greatest common factor(gcf) with different calculation methods (step-by-step) and by using calculator, formulas for every method, and several other gcf related terms.

But, let’s start with the basic definition!

Read on!

In Mathematics, the greatest common factor also known as greatest common denominator helps to determine the greatest integer which is divisible by each of the integers or give zero remainder. The highest common factor(HCF) or highest common divisor(HCD) is helpful in mathematics where it is necessary to determine the common factors of polynomials.

So, simply account this gcd calculator that allows you to estimate the greatest common divisor of your mathematical problems.

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.

Another method to find the gcf of the given data set is the prime factorization method. To find the gcf by prime factorization method, 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.

**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.

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 prime numbers have 2 positive factors while coprime numbers can be defined as “the numbers which have no common factors”. The highest common factor(HCF) of coprime numbers is 1.

For example; 5,7,35,48,23156 etc.

This simple online gcf calculator will help you to find the greatest common denominator (gcd) of two or n numbers. In other words: try this HCF calculator to determine the highest common factor for the given list of numbers, the tool shows step-by-step corresponding to the following methods:

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

Finding the greatest common multiple of numbers become very easy with accurate and free highest common factor(hcf) calculator. Just stick to these following steps to find the greatest common factor from this gcf finder.

Swipe on!

**Inputs:**

- First of all, you have to enter the numbers for which you want to calculate the (GCF).
- Then, select the gcf calculation method from the dropdown of this gcf calculator. It can either be “None(Simple)”,

“Listing factors”,” Prime factorization”,” Euclidean algorithm” or “Binary Stein’s algorithm”.

- Finally, hit the “gcf” button.

**Outputs:**

This greatest common divisor calculator will calculate the following:

- The Greatest Common Factor (GCF) of the numbers 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 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.

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. So this online gcf calculator allows you to find the greatest common divisor of the given problem.

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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