Common Factor Calculator
Find common factors and the Greatest Common Factor (GCF) of two or more numbers with detailed step-by-step solutions using multiple methods.
Enter Numbers
• Enter at least 2 positive integers
• Separate numbers with commas or spaces
• Example: 12, 18, 24
Results
Enter at least 2 numbers to find common factors
Methods to Find Common Factors
1. Listing Method
• List all factors of each number
• Find factors that appear in all lists
• The largest common factor is the GCF
• Good for smaller numbers
2. Prime Factorization
• Find prime factors of each number
• Take lowest powers of common primes
• Multiply to get GCF
• Efficient for larger numbers
3. Euclidean Algorithm
• For two numbers: GCD(a,b) = GCD(b, a mod b)
• Repeat until remainder is 0
• Very efficient for large numbers
• Extend to multiple numbers
4. Division Method
• Divide all numbers by small primes
• Continue until no common factors
• Multiply all common divisors
• Visual and systematic approach
Examples
Example 1: 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
Example 2: GCF of 24, 36, and 48
24 = 2³ × 3
36 = 2² × 3²
48 = 2⁴ × 3
GCF = 2² × 3 = 12
Applications
Fraction Simplification
Use GCF to reduce fractions to lowest terms by dividing both numerator and denominator by their GCF.
Problem Solving
Solve problems involving equal groups, arrangements, and finding the largest possible size of equal parts.
Ratios and Proportions
Simplify ratios by dividing all terms by their GCF to get the simplest form of the ratio.
Number Theory
Foundation for understanding divisibility, modular arithmetic, and various mathematical proofs.
Frequently Asked Questions
Common factors are positive integers that divide two or more numbers evenly (with no remainder). For example, the common factors of 12 and 18 are 1, 2, 3, and 6.
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.