GCF Calculator - Greatest Common Factor
Number 1
Number 2
Result
How to Use
- Enter two or more numbers (positive integers)
- Add more numbers if needed using the "Add Another Number" button
- Click "Calculate GCF" to find the greatest common factor
- The calculator will show the GCF and explain the calculation steps
What is the Greatest Common Factor (GCF)?
The Greatest Common Factor (GCF) of two or more numbers is the largest positive integer that divides each of the numbers without leaving a remainder. It's also known as the Greatest Common Divisor (GCD).
Example: GCF of 12 and 18
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Common factors: 1, 2, 3, 6
GCF = 6
Methods to Find GCF
| Method | Description | Example |
|---|---|---|
| Prime Factorization | Break numbers into prime factors and multiply common factors | 12 = 2² × 3 18 = 2 × 3² GCF = 2 × 3 = 6 |
| Euclidean Algorithm | Repeatedly divide larger number by smaller number | 18 ÷ 12 = 1 R6 12 ÷ 6 = 2 R0 GCF = 6 |
| Listing Factors | List all factors and find the largest common one | 12: 1,2,3,4,6,12 18: 1,2,3,6,9,18 GCF = 6 |
Applications
- Simplifying fractions
- Finding equivalent fractions
- Solving word problems
- Algebraic expressions
- Number theory
- Cryptography
Common Examples
| Numbers | GCF | Explanation |
|---|---|---|
| 8, 12 | 4 | Largest number that divides both 8 and 12 |
| 15, 20, 25 | 5 | Largest number that divides all three numbers |
| 7, 13 | 1 | Prime numbers have GCF of 1 |
| 24, 36, 48 | 12 | Largest common factor of all three numbers |
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