Greatest Common Factor Calculator
Calculate GCF & LCM
Results
| GCF (GCD) | — |
|---|---|
| LCM | — |
Step-by-step
How to Use This GCF Calculator
Reducing fractions and clearing common factors from algebra problems both start with the same question: what is the biggest whole number that divides every term? Paste your integers, get GCF and LCM together, and optionally read a prime-factor walkthrough when the values stay homework-sized.
- Enter at least two positive whole numbers. Separate with commas, spaces, tabs, or new lines—12, 18, 30 and 24 36 both parse.
- Press Calculate. The results table shows GCF (GCD) and LCM for the full list.
- Review step-by-step when shown. For inputs at or below 10 million, prime factorizations and exponent rules appear below the table.
- Use GCF to simplify. Divide each fraction part by the GCF, or pair with the LCM Calculator when denominators need alignment.
GCF Formulas and Practical Applications
Three classic paper methods match what the tool automates: list factors, prime-factor exponents, or repeated division (Euclidean algorithm). For long lists the engine folds pairwise GCF across every entry.
Prime factorization method
Write each number as a product of primes. For GCF, take each prime that appears in every factorization at its smallest exponent. Example: 12 = 2² × 3 and 18 = 2 × 3² share 2 × 3 = 6.
GCF and LCM link
GCF(a, b) × LCM(a, b) = a × b (two numbers)
This page prints both values because fraction work often needs GCF for simplifying and LCM for common denominators. The Fraction Calculator applies those ideas during add and subtract.
Where GCF shows up
- Reducing 24/36 to 2/3 by dividing top and bottom by 12.
- Factoring 6x + 9 as 3(2x + 3).
- Splitting items into equal largest group sizes without leftovers.
Standard Units and Conversion Tables
GCF and LCM are pure integers—no units apply. Inputs must be positive whole numbers from 1 up to 10 billion; zero, decimals, and negatives are rejected.
| Input rule | Behavior |
|---|---|
| Minimum count | At least two integers |
| Allowed separators | Comma, space, tab, newline |
| Max value | 10,000,000,000 per entry |
| Detailed steps | Shown when all values ≤ 10,000,000 |
To list every divisor of one number, use the Factor Calculator. Browse math calculators.
Frequently Asked Questions
What is the Greatest Common Factor (GCF)?
The largest integer dividing every number in your set evenly. Also called GCD or HCF.
How does GCF relate to LCM?
For two values, their product equals GCF × LCM. Both appear in the results table on this page.
Why does this calculator ask for positive whole numbers?
Integer factors are undefined for fractions and ambiguous for zero. The parser rejects non-whole input.
What if the GCF is 1?
The numbers are coprime—no shared factor beyond 1. The fraction is already fully reduced across those terms.
How do I simplify fractions using GCF?
Divide numerator and denominator by the GCF. For multi-step fraction arithmetic, open the Fraction Calculator.
Disclaimer. RapidRatio is informational only—not classroom policy or exam guidance. Verify requirements with your instructor.