Greatest common factor
The Greatest Common Factor (GCF) is the biggest number that can divide into two or more numbers without leaving a remainder. It's like finding the largest-sized group you can use to evenly split up different collections of items.
Concept
The Greatest Common Factor (GCF) is the largest factor that two or more numbers share. It's a useful tool for simplifying fractions and solving problems about grouping. **Method 1: Listing Factors** This is the most straightforward method for smaller numbers. 1. **List all the factors** for each number. 2. **Identify the common factors** that appear in both lists. 3. **Choose the greatest** of these common factors. **Example: Find the GCF of 12 and 18.** 1. **Factors of 12:** {1, 2, 3, 4, 6, 12} 2. **Factors of 18:** {1, 2, 3, 6, 9, 18} 3. **Common Factors:** {1, 2, 3, 6} 4. **Greatest Common Factor:** 6 **Method 2: Prime Factorization** This method is better for larger numbers. 1. **Find the prime factorization** of each number (break each number down to only prime numbers). A factor tree is great for this. 2. **Identify the common prime factors** that both numbers share. 3. **Multiply these common prime factors together** to get the GCF. **Example: Find the GCF of 48 and 60.** 1. **Prime Factorization:** * 48 = 2 x 2 x 2 x 2 x 3 * 60 = 2 x 2 x 3 x 5 2. **Common Prime Factors:** * Both numbers have two **2**s and one **3**. 3. **Multiply them:** * GCF = 2 x 2 x 3 = 12 **Visual Example:** Imagine you have 12 blue marbles and 18 red marbles. You want to put them into bags so that each bag has the same number of blue marbles and the same number of red marbles. The GCF (which is 6) tells you that the greatest number of bags you can make is 6. Each bag would have 2 blue marbles (12/6) and 3 red marbles (18/6). **Key Idea:** The GCF helps you find the most efficient way to break things down into equal groups.
Try it
Practice: Greatest common factor.