GCF Calculator Form
This is a free online calculator to find the GCF (Greatest Common Factor) of given two numbers.
How to Use This GCF Calculator
- Enter the first number in the input field labeled "First Number." For example, enter 24.
- Enter the second number in the input field labeled "Second Number." For instance, enter 36.
- Click the "Calculate GCF" button to find the greatest common factor of the two numbers.
- The calculator will apply the Euclidean Algorithm and display the GCF in the "Greatest Common Factor (GCF)" section below the input fields.
- If any input is invalid or less than or equal to zero, the calculator will prompt you to enter positive numeric values.
- The result will show the GCF of the two numbers. For example, if you entered 24 and 36, the GCF would be 12.
Using this simple GCF calculator will save you time and ensure that the correct greatest common factor is found quickly.
What is Meant by GCF?
The Greatest Common Factor (GCF), also known as the greatest common divisor (GCD), is the largest number that divides two or more integers without leaving a remainder. In simpler terms, it is the biggest number that can evenly divide both numbers. The GCF is useful for simplifying fractions, solving problems in arithmetic, and finding common factors between numbers.
For example, the GCF of 12 and 18 is 6 because 6 is the largest number that can divide both 12 and 18 evenly (without leaving a remainder).
How to Find the GCF
There are several methods to find the GCF of two numbers:
- Prime Factorization: Write the prime factors of both numbers and find the largest factor they share.
- Listing Factors: List out all the factors of each number and choose the greatest one that both numbers have in common.
- Euclidean Algorithm: This is a more efficient method for larger numbers. It involves dividing the numbers and using the remainder to find the GCF.
How to Find GCF of Two Numbers using Euclidean Algorithm on Paper
Follow these steps, to find the greatest common factor of any two numbers on paper using basic division and factorization methods.
- Write down the two numbers. For example, let’s use 48 and 18.
- Find the factors of each number. The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The factors of 18 are: 1, 2, 3, 6, 9, and 18.
- Identify the common factors. The common factors of 48 and 18 are: 1, 2, 3, and 6.
- Select the greatest common factor from the common factors. The GCF of 48 and 18 is 6.
- Alternatively, you can use the Euclidean Algorithm. Divide the larger number by the smaller number and take the remainder. Replace the larger number with the smaller number, and repeat the process until the remainder is zero. The last non-zero remainder is the GCF.
- For example, dividing 48 by 18 gives a remainder of 12. Dividing 18 by 12 gives a remainder of 6. Dividing 12 by 6 gives a remainder of 0, so the GCF is 6.
Examples
Example 1: Finding the GCF of 48 and 60
Let’s calculate the GCF of 48 and 60 using the Euclidean Algorithm.
Step 1: Divide 60 by 48
Since 60 is larger than 48, we start by dividing the larger number by the smaller number: \[ 60 \div 48 = 1 \quad \text{with a remainder of} \ 12 \]
Step 2: Replace and divide again
Now, replace 60 with 48 and 48 with the remainder from the previous step, which is 12. Divide: \[ 48 \div 12 = 4 \quad \text{with a remainder of} \ 0 \]
Step 3: The GCF is found
Since the remainder is now zero, the non-zero number (12) is the greatest common factor (GCF) of 48 and 60.
Example 2: Finding the GCF of 36 and 84
Now, let’s find the GCF of 36 and 84 using the Euclidean Algorithm.
Step 1: Divide 84 by 36
Divide the larger number (84) by the smaller number (36): \[ 84 \div 36 = 2 \quad \text{with a remainder of} \ 12 \]
Step 2: Replace and divide again
Replace 84 with 36 and 36 with the remainder (12). Divide: \[ 36 \div 12 = 3 \quad \text{with a remainder of} \ 0 \]
Step 3: The GCF is found
Since the remainder is zero, the non-zero number (12) is the greatest common factor (GCF) of 36 and 84.