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Free GCF calculator. Calculate Greatest Common Factor (GCF), Least Common Multiple (LCM), and prime factors with step-by-step solutions. Our calculator uses number theory principles to determine all factor relationships using the Euclidean algorithm.
Last updated: February 2, 2026
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12
Greatest Common Factor
72
Least Common Multiple
6
Total common factors
2
Numbers analyzed
24
2 × 2 × 2 × 3
36
2 × 2 × 3 × 3
Given: GCF of 24 and 36
Step 1: Apply Euclidean algorithm
Step 2: 24 = 36 × 0 + 24
Step 3: 36 = 24 × 1 + 12
Step 4: Continue until remainder is 0
Step 5: Last non-zero remainder is GCF = 12
Step 6: LCM = (24 × 36) / GCF = 72
Euclidean Algorithm
Euclidean algorithm for GCF calculation
Prime Factorization
Prime factorization method
LCM Calculation
LCM calculation using GCF
Method used
Euclidean Algorithm
Most efficient method
Method used
Iterative GCF
Multiple number analysis
Method used
Prime Factorization
Factor decomposition
Method used
Batch Processing
Multiple number analysis
Formula used
LCM = (a × b) / GCF
GCF-LCM relationship
Features
Complete Analysis
Comprehensive factor calculations
For GCF of 24 and 36:
GCF
12
LCM
72
Our GCF calculator uses the Euclidean algorithm and prime factorization to calculate Greatest Common Factor, Least Common Multiple, and prime factors. The calculation applies number theory principles and mathematical relationships to determine all factor properties.
Euclidean Algorithm: GCF(a,b) = GCF(b, a mod b)Prime Factorization: GCF = common prime factorsLCM Relationship: GCF × LCM = a × bThese methods form the foundation of number theory and allow determination of all factor relationships using efficient algorithms. They apply to all positive integers and provide both computational and theoretical insights.
Shows the relationship between GCF, LCM, and prime factors
The Greatest Common Factor is a fundamental concept in number theory that helps understand the divisibility relationships between numbers. It's essential for simplifying fractions, solving Diophantine equations, and understanding the structure of integers. The Euclidean algorithm provides an efficient way to compute GCF even for very large numbers.
Need help with other number theory calculations? Check out our LCM calculator and prime factorization calculator.
Get Custom Calculator for Your PlatformResult: GCF(24, 36) = 12, LCM(24, 36) = 72
The GCF is 12, which is the largest number that divides both 24 and 36 evenly.
24 = 2³ × 3, 36 = 2² × 3²
GCF = 2² × 3 = 12
24/36 simplified
24/36 = 2/3
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