Greatest Common Factor Calculator

Find the greatest common factor of two or more integers quickly and accurately.

▼ Enter numbers separated by commas and click Calculate

Numbers

Greatest Common Factor —

What Is the Greatest Common Factor (GCF)?

The greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest positive integer that divides two or more non-zero integers without leaving a remainder.

Example:
GCF(24, 36) = 12

Another example:
GCF(45, 60) = 15

The GCF is useful when simplifying fractions, finding common factors, and solving many problems involving integers.

Prime Factorization Method

One way to find the greatest common factor is to find the prime factorization of each number. The factors that are common to all the numbers are then multiplied together to find the GCF.

Example:
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
GCF(24, 36) = 2 × 2 × 3 = 12

Prime factorization is useful for smaller integers, but finding prime factors manually can become tedious for larger numbers.

Euclidean Algorithm

The Euclidean algorithm is an efficient method for finding the greatest common factor. It repeatedly divides one number by another and uses the remainder to continue the process until the remainder becomes zero.

Basic rules:
GCF(a, a) = a
GCF(a, b) = GCF(a − b, b), when a > b
GCF(a, b) = GCF(a, b − a), when b > a

Example:
GCF(48, 18)
48 = 18 × 2 + 12
18 = 12 × 1 + 6
12 = 6 × 2 + 0
Therefore, GCF(48, 18) = 6

For more than two integers, the same process can be repeated by finding the GCF of the next integer and the GCF obtained from the previous calculation.

How to Use the GCF Calculator

Step 1: Enter two or more integers separated by commas.

Step 2: Click the Calculate button.

Step 3: The calculator finds and displays the greatest common factor of all the numbers entered.

Frequently Asked Questions

What is the greatest common factor?

The greatest common factor (GCF) is the largest positive integer that divides two or more integers without leaving a remainder.

How many numbers can I enter?

You can enter two or more integers separated by commas. The calculator finds the GCF across all the numbers entered.

Can I enter negative numbers?

Yes. The calculator accepts negative integers and uses their absolute values when calculating the GCF.

What is the difference between GCF and GCD?

GCF and GCD refer to the same mathematical concept. Greatest Common Factor and Greatest Common Divisor are two commonly used names for the same value.

What is the Euclidean algorithm?

The Euclidean algorithm is an efficient method for finding the GCF by repeatedly using division and remainders until the remainder becomes zero.

Can the GCF be calculated for more than two numbers?

Yes. The calculator can find the GCF of multiple integers entered as a comma-separated list.

Disclaimer

This calculator is provided for general mathematical and educational purposes. While we aim to provide accurate results, SmartMyTools does not guarantee that the results are suitable for professional, academic, financial, engineering, or other specialized applications.