Greatest Common Factor (GCF) Calculator

Greatest Common Factor (GCF) is the largest number that divides evenly into two or more numbers.

Also called Greatest Common Divisor (GCD).

How to find the GCF using the Euclidean algorithm:

1. Divide the larger number by the smaller number
2. Take the remainder
3. Divide the previous divisor by the remainder
4. Repeat until the remainder is 0
5. The last non-zero remainder is the GCF

Example: GCF of 48 and 18

• 48 ÷ 18 = 2 remainder 12
• 18 ÷ 12 = 1 remainder 6
• 12 ÷ 6 = 2 remainder 0
• GCF = 6

Uses:

• Simplifying fractions (e.g., 48/18 becomes 8/3)
• Finding common denominators
• Solving ratio problems