What is Greatest Common Factor (GCF)

The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest integer that divides two or more numbers without leaving a remainder. For example, the GCF of 12 and 18 is 6, since 6 is the largest number that divides both 12 (\(\div 6 = 2\)) and 18 (\(\div 6 = 3\)).

How to Calculate Greatest Common Factor (GCF)

There are two common methods to find the GCF:

1. Listing Factors: List all factors of each number and identify the largest common one. For 24 and 36:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
GCF = 12

2. Prime Factorization: Break numbers into prime factors and multiply the common ones. For 30 and 45:
30 = \(2 \times 3 \times 5\)
45 = \(3^2 \times 5\)
GCF = \(3 \times 5 = 15\)

3. Euclidean Algorithm: Subtract or divide repeatedly. For 48 and 18:
\(48 \div 18 = 2\) remainder 12 ? \(18 \div 12 = 1\) remainder 6 ? \(12 \div 6 = 2\) remainder 0. GCF = 6.

Applications of GCF in Real Life

GCF is used in simplifying fractions, splitting objects into equal sections, and solving ratio problems. For instance, to divide a rectangular garden plot into equal square sections, the GCF of its length and width determines the largest square size. It’s also useful in scheduling recurring events or optimizing resource distribution.

Our Greatest Common Factor (GCF) Calculator

While understanding the math behind GCF is crucial, our online calculator simplifies the process for complex numbers. Enter values, and it applies algorithms like prime factorization or Euclidean method instantly. Use it to verify your manual calculations or save time on large numbers!