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Greatest Common Factor Calculator

179 words Calculator

Example Inputs:

Results

GCF of 24, 36, 48 is 12

Factors Breakdown

24

1234681224

36

123469121836

48

12346812162448

Easily calculate the GCF of multiple numbers with our free online tool. Find common factors, visualize results, and learn calculation methods (Euclidean algorithm or prime factorization) in seconds. Perfect for students, teachers, and math enthusiasts.

Greatest Common Factor Calculator

What is GCF?

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

  • Greatest Common Divisor (GCD)
  • Highest Common Factor (HCF)

Key Formulas

  1. ‌Euclidean Algorithm‌:
      GCF(a,b) = GCF(b, a mod b) until b=0
  2. ‌Prime Factorization‌:
    Multiply the lowest power of all common primes

How to Use

  1. Enter numbers (comma/space separated)
  2. Choose calculation method
  3. View results with:
    • Calculated GCF value
    • All factors listed
    • Visual factor comparison
  4. Toggle between Euclidean/Prime methods

FAQs

‌Q: How many numbers can I calculate?‌
A: The calculator supports 2-10 numbers simultaneously.

‌Q: Which method is faster?‌
A: Euclidean algorithm is generally more efficient for large numbers.

‌Q: Can I see step-by-step solutions?‌
A: Yes! Enable “Show Steps” for detailed calculations.

Terminology

  • ‌Factor‌: A number that divides another exactly (e.g., 3 is a factor of 12)
  • ‌Common Factor‌: A factor shared by multiple numbers
  • ‌Modulo Operation‌: The remainder after division (a mod b)
  • ‌Prime Number‌: A number with exactly two factors (1 and itself)
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