HOW TO read prime factor steps?

Switch on "Show prime factor steps" to see each number's prime factors, common primes, and the product forming the GCF.

HOW TO read prime factor steps?

Switch on "Show prime factor steps" to see each number's prime factors, common primes, and the product forming the GCF.

Greatest Common Factor Calculator | GCF Solver (Fast & Mobile-Friendly)

Greatest Common Factor Calculator

Find the GCF (HCF/GCD) of two or more integers with prime factors and Euclidean steps — responsive and global.

Enter integers (comma, space, or newline separated)

Numbers

Enter integers only. Negative values are accepted and treated by absolute value. Zero handling explained below.

Display mode

Choose how detailed the steps should be.

Tip: GCF(0, n) = |n| when only one non-zero number; GCF(0,0) = 0 by convention in this tool.

Understanding the Greatest Common Factor (GCF)

The Greatest Common Factor (GCF), also called Highest Common Factor (HCF) or Greatest Common Divisor (GCD), is the largest positive integer that divides each of the given integers without leaving a remainder. GCF is fundamental in simplifying fractions, solving Diophantine equations, working with ratios, and many algorithmic problems.

Methods to find GCF

Euclidean algorithm: Repeatedly apply GCD(a, b) = GCD(b, a mod b) until remainder is zero. It's fast and efficient for large integers.

Prime factorization: Factor each number into primes, then multiply the common primes raised to their minimum exponents across numbers.

Pairwise reduction: For multiple numbers compute GCF iteratively: GCF(a,b,c) = GCF(GCF(a,b),c).

Edge cases and rules

Zero handling: GCF(0, n) = |n|; GCF(0,0) = 0 by convention in this calculator.

Negatives: GCF uses absolute values; sign does not affect GCF magnitude.

Large numbers: Euclidean algorithm handles very large numbers efficiently; prime-factor mode is educational and may show large primes when present.

Who benefits

Students: Homework, exam prep, fraction simplification, and learning number theory basics.

Teachers: Demonstrate Euclidean algorithm and prime-factor methods step-by-step.

Developers & analysts: Use GCF for algorithmic simplifications, ratios, and discrete math tasks.

FAQs

HOW TO find the GCF of two numbers?

Enter the two numbers separated by commas and click Calculate. The tool shows the GCF and, if requested, step-by-step prime-factor or Euclidean steps.

HOW TO compute GCF of multiple numbers?

Enter all numbers separated by commas or new lines. The calculator computes pairwise GCD iteratively and displays the final GCF.

HOW TO interpret prime factor steps?

Switch to "Show prime factor steps" to see each number's prime factors, identify common primes, take minimum exponents, and multiply them to get the GCF.

HOW TO reset the calculator?

Click Reset to clear inputs, messages, and results instantly. You can also use the sample button to load example numbers.

HOW TO use this tool globally?

The tool is client-side, uses standard mathematical notation, and requires no locale settings. It works the same on phones, tablets, laptops, and desktops worldwide.

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