Greatest Common Factor (GCF) Calculator

Find the Greatest Common Factor with Step-by-Step Solutions

Calculate the GCF of two positive integers using prime factorization. Common factors are highlighted in red.
What is the Greatest Common Factor?

The Greatest Common Factor (GCF) is the largest positive integer that divides two or more numbers without a remainder.

Method: Find the prime factorization of each number, then multiply the common prime factors.

Example: Find GCF of 40 and 60
40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
Common factors: 2 × 2 × 5 = 20
GCF(40, 60) = 20
Enter positive integers (greater than 0).
Greatest Common Factor
—
Enter two positive integers and click "Find GCF"
Step-by-step solution will appear here after calculation.

Applications of GCF

  • Reducing Fractions: Divide numerator and denominator by their GCF to simplify fractions.
  • Factoring Expressions: Factor out the GCF from algebraic expressions.
  • Solving Problems: Find the largest equal groups, dimensions, etc.

More References and Links