What is the greatest common factor for the numbers 24, 36, and 60?

To find the **Greatest Common Factor (GCF)** of the numbers **24**, **36**, and **60**, you can use several methods. Below, I'll demonstrate two common approaches: **Listing Factors** and **Prime Factorization**. --- ### Method 1: Listing Factors **Step 1: List all factors of each number.** - **Factors of 24:** 1, 2, 3, 4, 6, 8, 12, **24** - **Factors of 36:** 1, 2, 3, 4, 6, 9, 12, 18, **36** - **Factors of 60:** 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, **60** **Step 2: Identify the common factors.** - Common factors of **24, 36, and 60** are: **1, 2, 3, 4, 6, 12** **Step 3: Determine the greatest of these common factors.** - The **Greatest Common Factor (GCF)** is **12**. --- ### Method 2: Prime Factorization **Step 1: Find the prime factors of each number.** - **Prime factors of 24:** \(24 = 2^3 \times 3^1\) - **Prime factors of 36:** \(36 = 2^2 \times 3^2\) - **Prime factors of 60:** \(60 = 2^2 \times 3^1 \times 5^1\) **Step 2: Identify the common prime factors with the smallest exponents.** - **Common prime factors:** - **2:** The smallest exponent among the three numbers is \(2^2\). - **3:** The smallest exponent among the three numbers is \(3^1\). **Step 3: Multiply these common prime factors together to find the GCF.** - \(GCF = 2^2 \times 3^1 = 4 \times 3 = 12\) --- ### Conclusion Using either method, the **Greatest Common Factor (GCF)** of **24**, **36**, and **60** is **12**.