What is the Greatest Common Factor (GCF)?
The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF), is the largest positive integer that divides evenly into all numbers with zero remainder. For example, the GCF of 12 and 18 is 6.
Prime Factorization Method
To find the GCF using prime factorization:
- Find the prime factors of each number.
- Identify the common prime factors.
- Multiply these common factors together.
Example: GCF(12, 18)
12 = 2 × 2 × 3
18 = 2 × 3 × 3
Common factors: 2 and 3.
GCF = 2 × 3 = 6.
Euclidean Algorithm
An efficient method for finding the GCF of two numbers is the Euclidean Algorithm, which uses the principle that the GCF of two numbers also divides their difference.