GCF Calculator
Calculate the Greatest Common Factor (GCF) of two or more numbers with step-by-step calculations using the Euclidean algorithm. Perfect for simplifying fractions and solving math problems.
Calculate Greatest Common Factor
Common GCF Calculations
Click on these links to see instant calculations with common number sets:
Greatest Common Factor (GCF)
The Greatest Common Factor (GCF), also known as Greatest Common Divisor (GCD), is the largest positive integer that divides each of the given numbers without leaving a remainder.
GCF Calculation Methods
Prime Factorization: Find common prime factors and multiply
Listing Method: List factors of each number and find the largest common one
Example: GCF(12, 18) = 6 (largest number that divides both 12 and 18)
Common GCF Examples
| Numbers | GCF | Method | Application |
|---|---|---|---|
| 12, 18 | 6 | 6 divides both | Simplify 12/18 = 2/3 |
| 24, 36 | 12 | 12 divides both | Simplify 24/36 = 2/3 |
| 15, 25, 35 | 5 | 5 divides all three | Factor out 5 |
| 48, 72 | 24 | 24 divides both | Simplify 48/72 = 2/3 |
| 7, 11 | 1 | Both are prime | Already coprime |
- Fraction Simplification: Reduce fractions to lowest terms by dividing by GCF
- Problem Solving: Find common denominators and solve ratio problems
- Algebra: Factor polynomials and simplify algebraic expressions
- Number Theory: Study relationships between numbers and divisibility
- Real-world Applications: Organize items into equal groups, tile patterns
Frequently Asked Questions
What is the greatest common factor (GCF)?
The greatest common factor (GCF), also called greatest common divisor (GCD), is the largest positive integer that divides each of the given numbers without a remainder.
How do you find the GCF of two numbers?
You can find the GCF using the Euclidean algorithm: repeatedly divide the larger number by the smaller number and replace the larger with the remainder until the remainder is 0. The last non-zero remainder is the GCF.
What is the difference between GCF and LCM?
GCF (Greatest Common Factor) is the largest number that divides all given numbers, while LCM (Least Common Multiple) is the smallest number that all given numbers divide into.