Greatest Common Factor Calculator
How to Use the ‘Greatest Common Factor Calculator’?
Follow these steps to use the greatest common factor calculator:
Step 1: Enter the known numbers using a comma between them into the input box.
Step 2: Click on the ‘Solve’ button to obtain the GCF.
Step 3: Choose a specific method of calculating the GCF from the dropdown box.
Step 4: Click on the ‘Show Steps’ button to view the steps leading to the solution of calculating the greatest common factor.
Step 5: Click on the 
button to enter new inputs and start again.
Step 6: Click on the ‘Example’ button to input random values.
Step 7: Click on the ‘Explore’ button to select two different numbers and obtain their factors, LCM and GCF.
Step 8: When on the ‘Explore’ page, click the ‘Calculate’ button, if you want to go back to the calculator.
What Is the Greatest Common Factor?
The greatest common factor of two or more numbers is the greatest ‘nonzero’ number among the common factors of the given numbers. The term greatest common factor is often abbreviated as GCF. It is also called the greatest common denominator (GCD).
Methods Used to Find the Greatest Common Factor Calculator:
There are two basic methods to calculate the GCF of two or more numbers.
- Listing factors:
This method contains the following steps:
Step 1: List the factors of each number
Step 2: Highlight and list the common factors
Step 3: The highest among the common factors is the GCF of the given numbers
- Prime Factorization:
This method contains the following steps:
Step 1: Write numbers as the product of its prime factors
Step 2: List the prime factors that are common in the prime factorization of numbers
Step 3: The product of the common prime factors is the GCF of the given numbers
Note: The GCF of numbers with no common prime factors is always 1.
Solved Examples
Example 1: Find the greatest common factor of 100 and 150 by listing the factors of these two numbers.
Solution:
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
The common factors are: 1, 2, 5, 10, 25, 50
The greatest among these is 50.
Hence, the greatest common factor of 100 and 150 is 50.
Example 2: Find the greatest common factor of 20, 12 and 32 by listing the factors of these numbers.
Solution:
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 32: 1, 2, 4, 8, 16, 32
The common factors are 1, 2, 4
The greatest among these is 4.
Hence, the greatest common factor of 20, 12 and 32 is 4.
Example 3: Find the greatest common factor of 80 and 125 by applying the prime factorization method.
Solution:
Write each number as a product of prime factors:
\(80 = 2 \times 2 \times 2 \times 2 \times 5\)
\(125 = 5 \times 5 \times 5\)
The common prime factor is: 5
Hence, the GCF of 80 and 125 is 5.
Example 4: Find the greatest common factor of 15, 50 and 75 using the prime factorization method.
Solution:
Write each number as a product of prime factors:
\(15 = 3 \times 5\)
\(45 = 3 \times 3 \times 5\)
\(75 = 3 \times 5 \times 5\)
The common prime factors are \( 3 \times 5 \)
Hence, the GCF of 15, 45 and 75 is 15.
Example 5: Calculate the GCF of 51 and 52.
Solution:
Write each number as a product of prime factors:
\(51 = 3 \times 17\)
\(52 = 2 \times 2 \times 13\)
There are no common prime factors.
Hence, the GCF of 51 and 52 is 1.
The factors of a number is a collection of numbers that divides the given number completely. The number can also be written as the product of its factors. For example, the factors of 20 are 1, 2, 4, 5, 10, and 20.
When a number is multiplied by any natural number the product obtained is a multiple of the given number.
GCF is the greatest among the factors of the given numbers. Here, co-prime numbers are numbers that have no common factors, except 1. Therefore, the greatest common factor of two co-prime numbers is always 1.
The least common multiple of two numbers is the smallest number that is divisible by both numbers. For example, the LCM of 10 and 15 is 30. As 30 is the smallest number that is divisible by both 10 and 15.