Greatest Common Factor (GCF) Calculator
Enter two or more numbers separated by commas to calculate the **GCF (Greatest Common Factor)**.
GCF:
GCF Calculator - A Complete Guide
The **Greatest Common Factor (GCF)**, also known as the **Highest Common Factor (HCF)**, is the largest number that divides two or more numbers without leaving a remainder.
How to Find the GCF?
There are multiple ways to find the **GCF**:
- Prime Factorization Method: Find the prime factors of each number and multiply the common factors.
- Division Method: Use the **Euclidean algorithm**, which finds the GCF by repeated division.
- List of Factors Method: List out all the factors and find the greatest common one.
Example Calculations
Example 1: Find the **GCF of 24 and 36**.
Prime factors of **24**: 2 × 2 × 2 × 3
Prime factors of **36**: 2 × 2 × 3 × 3
Common factors: **2 × 2 × 3 = 12**
GCF(24, 36) = 12
Example 2: Find the **GCF of 48, 64, and 80**.
Prime factors of **48**: 2 × 2 × 2 × 2 × 3
Prime factors of **64**: 2 × 2 × 2 × 2 × 2 × 2
Prime factors of **80**: 2 × 2 × 2 × 2 × 5
Common factors: **2 × 2 × 2 × 2 = 16**
GCF(48, 64, 80) = 16
Real-Life Applications of GCF
- Used in **simplifying fractions**.
- Essential in **math, engineering, and data analysis**.
- Helps in **solving problems related to equal grouping or division**.
Formula Reference
✔ **Prime Factorization Method:** Find the common prime factors and multiply them.
✔ **Euclidean Algorithm:** \( GCF(a, b) = GCF(b, a \mod b) \)
Our **GCF Calculator** quickly finds the **Greatest Common Factor** of multiple numbers, making it an essential tool for students, teachers, and professionals.
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