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Free common factor calculator. Calculate greatest common factor, least common multiple, and common factors of numbers with step-by-step solutions. Our calculator uses number theory principles to determine all factor relationships from any given inputs.
Last updated: February 2, 2026
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Enter 2 or more numbers separated by commas
6
Greatest Common Factor
72
Least Common Multiple
4
Total common factors
Input numbers: 12, 18, 24
Prime factors: 12 = 2 × 2 × 3, 18 = 2 × 3 × 3, 24 = 2 × 2 × 2 × 3
All factors: 12: [1, 2, 3, 4, 6, 12], 18: [1, 2, 3, 6, 9, 18], 24: [1, 2, 3, 4, 6, 8, 12, 24]
Common factors: [1, 2, 3, 6]
Greatest Common Factor (GCF): 6
Least Common Multiple (LCM): 72
Factor Listing
List all factors and find common ones
Prime Factorization
Factor each number into primes and find common factors
Euclidean Algorithm
Use Euclidean algorithm for efficient calculation
Method used
Euclidean Algorithm
Efficiently finds the largest common divisor
Formula used
LCM = (a × b) / GCF(a, b)
Uses GCF relationship for efficient calculation
Method used
Factor Listing
Lists all common divisors
Method used
Trial Division
Systematic prime factorization
Method used
Systematic Search
Finds all factor combinations
Features
Comprehensive Analysis
Complete number theory calculations
For numbers 12, 18, 24:
GCF
6
LCM
72
Common Factors
4
Our common factor calculator uses the fundamental principles of number theory to calculate all factor relationships from any given inputs. The calculation applies mathematical algorithms and number theory to determine GCF, LCM, and common factors.
GCF(a,b) = GCF(b, a mod b)LCM(a,b) = (a × b) / GCF(a,b)Common Factors = ∩(Factors of each number)Prime Factors = Trial DivisionThese formulas form the foundation of number theory analysis and allow calculation of all factor relationships from any combination of known values. They apply to both small and large numbers efficiently.
Shows the relationships between GCF, LCM, and common factors
Common factors are fundamental concepts in number theory that describe the relationships between numbers. They are essential for understanding divisibility, fractions, and many mathematical applications in algebra, geometry, and advanced mathematics.
Need help with other number theory calculations? Check out our GCF calculator and LCM calculator.
Get Custom Calculator for Your PlatformResult: GCF = 6, LCM = 72, Common Factors = [1, 2, 3, 6]
The numbers 12, 18, and 24 have a greatest common factor of 6 and least common multiple of 72.
Numbers: 15, 25
GCF = 5, LCM = 75
Numbers: 7, 11, 13
GCF = 1, LCM = 1001
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