Common Factor Calculator
Find all common factors and the greatest common factor (GCF) of numbers
Input Numbers
Enter at least 2 positive integers to find their common factors
How to Find Common Factors
Step 1: Find all factors of each number
Step 2: Identify factors that appear in all lists
Step 3: The largest common factor is the GCF
Example: For 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
• 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
Applications
- Simplifying fractions to lowest terms
- Finding common denominators
- Solving problems involving ratios
- Dividing objects into equal groups
- Pattern recognition in mathematics
- Algebraic factorization
- Number theory problems
- Cryptography and security
Properties of Common Factors
Key Properties:
- • 1 is always a common factor of any set of integers
- • The GCF is the largest common factor
- • Common factors divide the GCF evenly
- • For coprime numbers, GCF = 1
Relationships:
- • GCF(a,b) × LCM(a,b) = a × b
- • GCF(a,b) ≤ min(a,b)
- • If a|b, then GCF(a,b) = a
- • GCF(a,b,c) = GCF(GCF(a,b),c)