Greatest Common Factor Calculator
Find the GCF using multiple methods with step-by-step solutions and visualizations
Greatest Common Factor Calculator
Result
Greatest Common Factor
6
GCF of 12, 18
Euclidean Algorithm
Visual Representation
Euclidean Algorithm
The Euclidean algorithm uses repeated division to find the GCD efficiently. See the step-by-step solution for detailed calculations.
Step-by-Step Solution
- Starting with the first number: 12
- Finding GCD(12, 18):
- 12 = 18 × 0 + 12
- 18 = 12 × 1 + 6
- 12 = 6 × 2 + 0
- GCD(12, 18) = 6
Factor Analysis
All Common Factors: 1, 2, 3, 6
What is Greatest Common Factor Calculator?
What is the Greatest Common Factor?
The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides all given numbers without leaving a remainder.
Methods to Find GCF
1. Euclidean Algorithm
Most efficient method using repeated division. For two numbers a and b:
- Divide a by b and get remainder r
- Replace a with b and b with r
- Repeat until remainder is 0
- The last non-zero remainder is the GCF
2. Prime Factorization
Break each number into prime factors and find common ones:
- Find prime factorization of each number
- Identify common prime factors
- Take the minimum power of each common prime
- Multiply these together to get the GCF
3. Listing Factors
List all factors of each number and find the largest common one:
- List all factors of each number
- Find factors that appear in all lists
- The largest common factor is the GCF
Applications
- Simplifying fractions to lowest terms
- Finding common denominators
- Solving problems involving equal groups or arrangements
- Computer science algorithms and cryptography
FAQ - Greatest Common Factor Calculator
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.