Common Factors vs. Greatest Common Factor (GCF) Explained

📚 Quick Study Guide

🔍 Factors are numbers that divide evenly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. ➕ Common factors are factors that two or more numbers share. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors of 12 and 18 are 1, 2, 3, and 6. ➗ The greatest common factor (GCF) is the largest of the common factors. In the example above, the GCF of 12 and 18 is 6. 💡 To find the GCF, list the factors of each number and identify the largest factor they have in common. ➗ Another method to find the GCF is prime factorization. Break down each number into its prime factors, then multiply the common prime factors together. For example: * 12 = 2 x 2 x 3 * 18 = 2 x 3 x 3 * GCF = 2 x 3 = 6 📝 The GCF is useful for simplifying fractions and solving various mathematical problems.

Practice Quiz

1. What are the factors of 20?
   1. 1, 2, 4, 5, 10, 20
   2. 1, 2, 3, 5, 10, 20
   3. 2, 4, 5, 10, 15, 20
   4. 1, 5, 10, 15, 20, 25
2. What are the factors of 36?
   1. 1, 2, 3, 4, 6, 9, 12, 18, 36
   2. 1, 2, 3, 4, 5, 6, 9, 12, 18
   3. 2, 3, 4, 6, 8, 9, 12, 18, 36
   4. 3, 6, 9, 12, 15, 18, 36
3. What are the common factors of 16 and 24?
   1. 1, 2, 4, 8
   2. 1, 2, 3, 4
   3. 2, 4, 6, 8
   4. 1, 3, 6, 8
4. What is the Greatest Common Factor (GCF) of 15 and 25?
   1. 5
   2. 3
   3. 10
   4. 15
5. What is the GCF of 24 and 36?
   1. 12
   2. 6
   3. 8
   4. 4
6. What is the GCF of 42 and 63?
   1. 21
   2. 7
   3. 14
   4. 9
7. What is the GCF of 18, 24, and 30?
   1. 6
   2. 3
   3. 9
   4. 12