Greatest Common Factor Calculator
Find the greatest common factor (GCF) of two numbers. Also known as the greatest common divisor (GCD) or highest common factor (HCF).
Gcf
12
Formule
## How to Find the Greatest Common Factor ### Methods **Method 1: Prime Factorization** 1. Find the prime factors of each number 2. Identify the common prime factors 3. Multiply the common factors together **Method 2: Euclidean Algorithm** 1. Divide the larger number by the smaller 2. Replace the larger number with the remainder 3. Repeat until the remainder is 0 4. The last non-zero remainder is the GCF ### Useful Identity **GCF(a, b) × LCM(a, b) = a × b**
Exemple Résolu
Find the GCF of 48 and 36.
- 01Prime factorization of 48: 2⁴ × 3 = 2 × 2 × 2 × 2 × 3
- 02Prime factorization of 36: 2² × 3² = 2 × 2 × 3 × 3
- 03Common factors: 2² × 3 = 4 × 3
- 04GCF(48, 36) = 12
Questions Fréquentes
What is the GCF?
The greatest common factor (GCF) of two numbers is the largest number that divides both of them evenly. For example, GCF(12, 18) = 6.
How is the GCF related to simplifying fractions?
To simplify a fraction, divide both the numerator and denominator by their GCF. For example, 12/18: GCF = 6, so 12/18 = 2/3.
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