GCF Calculator
Find the Greatest Common Factor (GCF / GCD / HCF) of any set of numbers with step-by-step Euclidean algorithm divisions.
Input Parameters
Live Result
Details
Steps
Factorize each number into prime factors
GCF (Greatest Common Factor): Multiply common prime factors with lowest exponents
LCM (Least Common Multiple): Multiply all prime factors with highest exponents
Quick Answer & Understanding Your Result
A GCF Calculator finds the Greatest Common Factor (GCF)—also known as Greatest Common Divisor (GCD) or Highest Common Factor (HCF)—of two or more integer values.
Classical Factorization Methods
- Euclidean Algorithm (Division Remainder): Successively divides larger integers by smaller remainders until the remainder reaches zero (a = bq + r).
- Prime Factorization Method: Decomposes each integer into prime factors and multiplies the lowest powers of all shared prime factors.
- Multi-Number Support: Computes common divisors across 3, 4, or more integers simultaneously ( GCF(a, b, c) = GCF( GCF(a, b), c)).
Algebraic & Engineering Applications
- Fraction Simplification: Dividing numerator and denominator by their GCF to reduce to lowest terms.
- Tiling & Packaging Optimization: Determining optimal square tile dimensions without cutting material.
Enter your numbers above to calculate the GCF and step-by-step Euclidean division table instantly.
Formula & Calculation Logic
Mathematical FormulaEuclidean Algorithm steps:
- Divide a by b to get remainder r.
- Replace (a, b) with (b, r) and repeat until r = 0.
- The final non-zero divisor is the Greatest Common Factor.
Step-by-Step Guide
Enter Numbers
Input two or more positive integers separated by commas (e.g. 48, 64).
Euclidean Division Execution
The algorithm calculates prime factors and Euclidean steps in real time.
View GCF & Step Solver
Receive the greatest common divisor and detailed factor tree.
Worked Examples Table
| Example | Input Values | Calculated Result | Explanation |
|---|---|---|---|
| GCF of 48 and 64 | 64 mod 48 = 16; 48 mod 16 = 0. The GCF is 16. | ||
| 18, 24 (GCF: 6, LCM: 72) | Provides instant quantitative evaluation for comparative practical analysis. |
Frequently Asked Questions
Evidence-Based Methodology & Authoritative References
Euclid's Elements - Book VII: Number Theory
NIST Digital Library of Mathematical Functions - Integer Arithmetic
Standard: ISO / W3C / IETF Authoritative Domain Standard
Formula: GCF(a, b) = GCF(b, a mod b) until (a mod b) = 0
Last Reviewed: August 21, 2026
Primary Source: Euclid's Elements - Book VII: Number Theory
Reference Document: NIST Digital Library of Mathematical Functions - Integer Arithmetic
Computation Privacy: 100% client-side 0ms computation, zero data retention
Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.
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Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.