Greatest Common Factor Calculator
Find the greatest common factor (GCF/HCD) of two or more whole numbers instantly.
Greatest Common Factor Calculator
Find the greatest common factor (GCF/HCD) of two or more whole numbers instantly.
How to use the Greatest Common Factor Calculator
- Enter two or more whole numbers separated by commas.
- Click Calculate.
Formula
GCF(a, b) via Euclidean algorithm:
GCF(a, b) = GCF(b, a mod b) until b = 0
Example
GCF of 48 and 36: GCF(48,36) = GCF(36,12) = GCF(12,0) = 12
Step-by-step calculation
- Apply Euclidean algorithm: 48 mod 36 = 12.
- Next: 36 mod 12 = 0.
- When remainder is 0, the divisor is the GCF: 12.
Real-world uses
- Simplifying fractions.
- Factoring algebraic expressions.
- Finding evenly divisible group sizes.
Common mistakes
- Entering decimal numbers instead of whole numbers.
- Confusing GCF with LCM.
- Assuming GCF is always 1 (it can be larger).
Frequently asked questions
What if the GCF is 1?
The numbers are called "coprime" or "relatively prime" — they share no common factors other than 1.
Can I find the GCF of more than two numbers?
Yes. Enter as many numbers as needed, separated by commas.
What is the difference between GCF and LCM?
GCF is the largest factor dividing all numbers. LCM is the smallest multiple all numbers divide into.