Greatest Common Factor Calculator

Use this calculator to find the greatest common factor (GCF) of two or more numbers. Get step-by-step solutions and understand how GCF is calculated.

Greatest Common Factor Calculator

Enter two or more numbers separated by commas, then click Calculate to find their greatest common factor (GCF).

Result

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 numbers without a remainder.

For example, the GCF of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 evenly.

Methods to Find the GCF

Euclidean Algorithm

This method uses repeated division to find the GCF. It's based on the principle that if a and b are two positive integers, then GCF(a,b) = GCF(b, a mod b).

Example: To find GCF(48, 18)
1. Divide: 48 ÷ 18 = 2 remainder 12
2. Replace: GCF(48, 18) = GCF(18, 12)
3. Divide: 18 ÷ 12 = 1 remainder 6
4. Replace: GCF(18, 12) = GCF(12, 6)
5. Divide: 12 ÷ 6 = 2 remainder 0
6. When remainder is 0, the divisor (6) is the GCF
Therefore, GCF(48, 18) = 6

Prime Factorization Method

This method involves finding the prime factorization of each number, then multiplying the common prime factors with their lowest powers.

Example: To find GCF(12, 18)
1. Prime factorization: 12 = 2² × 3, 18 = 2 × 3²
2. Common factors: 2¹ and 3¹ (lowest powers)
3. Multiply them: 2¹ × 3¹ = 2 × 3 = 6
Therefore, GCF(12, 18) = 6

Applications of GCF

  • Simplifying fractions to their lowest terms
  • Finding the largest possible size for equal groups or portions
  • Solving problems in number theory and cryptography
  • Reducing measurements to their simplest form in engineering and design

How to Use This Calculator

  1. Enter two or more positive integers separated by commas in the input field.
  2. Click the 'Calculate' button to find the GCF.
  3. View the result and the step-by-step solution explaining how the GCF was calculated.
  4. Click 'Clear' to reset the calculator and perform a new calculation.