How Does Prime Factorization Help Find the Greatest Common Factor?

📚 Quick Study Guide

🔍 Prime Factorization: Breaking down a number into its prime factors (e.g., $12 = 2 \times 2 \times 3$).

➕ Greatest Common Factor (GCF): The largest number that divides two or more numbers without leaving a remainder.

💡 Steps to Find GCF Using Prime Factorization:
• 1️⃣ Find the prime factorization of each number.
• 2️⃣ Identify the common prime factors.
• 3️⃣ Multiply the common prime factors together.

Practice Quiz

1. Question 1: What is the prime factorization of 24?
   1. A. $2 \times 3 \times 4$
   2. B. $2 \times 2 \times 2 \times 3$
   3. C. $4 \times 6$
   4. D. $2 \times 2 \times 6$
2. Question 2: What is the prime factorization of 36?
   1. A. $4 \times 9$
   2. B. $2 \times 2 \times 3 \times 3$
   3. C. $6 \times 6$
   4. D. $2 \times 3 \times 6$
3. Question 3: What are the common prime factors of 24 and 36?
   1. A. 2 and 3
   2. B. 4 and 6
   3. C. 2, 3, and 4
   4. D. 6 and 12
4. Question 4: What is the GCF of 24 and 36?
   1. A. 6
   2. B. 12
   3. C. 4
   4. D. 24
5. Question 5: Find the prime factorization of 48.
   1. A. $6 \times 8$
   2. B. $2 \times 2 \times 2 \times 2 \times 3$
   3. C. $4 \times 12$
   4. D. $2 \times 3 \times 8$
6. Question 6: Find the GCF of 48 and 36.
   1. A. 6
   2. B. 12
   3. C. 24
   4. D. 4
7. Question 7: What is the GCF of 15 and 25?
   1. A. 1
   2. B. 3
   3. C. 5
   4. D. 25