Greatest Common Factor (GCF) Calculator

Greatest Common Factor (GCF) Calculator

Calculate the Greatest Common Factor (GCF) of two or more numbers. Enter numbers separated by commas to find their GCF with step-by-step factorization.

GCF Result

Prime Factorization

Calculation Steps

Common Factors

Number Factors Common Factors

Factor Visualization

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 each of the numbers without leaving a remainder. For example, the GCF of 12 and 18 is 6.

Example: Find GCF of 12 and 18

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

Common factors: 1, 2, 3, 6

GCF = 6

How to Calculate GCF

There are several methods to find the GCF:

  • Listing Factors: List all factors of each number and find the largest common one
  • Prime Factorization: Factor each number into primes and multiply the common prime factors
  • Euclidean Algorithm: Repeatedly apply the formula GCF(a, b) = GCF(b, a mod b) until b = 0

Applications of GCF

  • Mathematics: Simplifying fractions, solving equations, number theory
  • Engineering: Ratio calculations, scaling designs
  • Computer Science: Algorithm optimization, cryptography
  • Everyday Life: Dividing items into equal groups, scheduling events

How to Use This Calculator

  • Enter two or more numbers separated by commas
  • Click “Calculate GCF” to see the result and step-by-step solution
  • View the prime factorization of each number
  • See all common factors in a table
  • Visualize the factors with an interactive chart
  • Copy or download your results for future reference

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