Understand factors and factor pairs
Factors are the numbers you multiply together to get another number! Finding factors is like solving a puzzle - which numbers fit together perfectly?
Concept
Factors are building blocks of numbers! 🎯 **What Are Factors?** Factors of a number are all the whole numbers that divide into it evenly (with no remainder). **Example: Factors of 12** Which numbers divide evenly into 12? • 12 ÷ 1 = 12 ✓ • 12 ÷ 2 = 6 ✓ • 12 ÷ 3 = 4 ✓ • 12 ÷ 4 = 3 ✓ • 12 ÷ 5 = 2.4 ✗ (not a whole number) • 12 ÷ 6 = 2 ✓ • 12 ÷ 12 = 1 ✓ Factors of 12: **1, 2, 3, 4, 6, 12** 💡 **Factor Pairs:** Factor pairs are two numbers that multiply to give you the original number. Factor pairs of 12: • 1 × 12 = 12 • 2 × 6 = 12 • 3 × 4 = 12 Notice: Each factor appears in a pair! 🔍 **Finding Factor Pairs Systematically:** For 24: • Start with 1: 1 × 24 = 24 ✓ • Try 2: 2 × 12 = 24 ✓ • Try 3: 3 × 8 = 24 ✓ • Try 4: 4 × 6 = 24 ✓ • Try 5: Doesn't work evenly • Stop when numbers repeat! Factor pairs of 24: (1,24), (2,12), (3,8), (4,6) All factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 🌟 **Special Facts:** • 1 is a factor of EVERY number • Every number is a factor of itself • Even numbers always have 2 as a factor • Numbers with an odd number of factors are perfect squares! 🎨 **Array Model:** You can show factor pairs with arrays! 12 can be arranged as: • 1 row of 12: ●●●●●●●●●●●● • 2 rows of 6: ●●●●●● ●●●●●● • 3 rows of 4: ●●●● ●●●● ●●●●
Try it
Practice finding factors and factor pairs! 📝 **List All Factors:** 1. Find all factors of 18 2. Find all factors of 20 3. Find all factors of 30 4. Find all factors of 16 🔢 **Find Factor Pairs:** 5. List all factor pairs of 24 6. List all factor pairs of 36 7. List all factor pairs of 28 🎯 **True or False:** 8. 4 is a factor of 32 (True/False) 9. 7 is a factor of 56 (True/False) 10. 5 is a factor of 27 (True/False) 🎨 **Missing Factor:** 11. 3 × ___ = 24 (Find the missing factor) 12. ___ × 7 = 42 13. 8 × ___ = 64 🏆 **Word Problems:** 14. You have 18 chairs to arrange in equal rows. What are all the possible arrangements? (Use factor pairs!) 15. A rectangle has an area of 36 square units. What are all the possible whole number dimensions? 💪 **Challenge:** 16. What number less than 30 has the most factors? 17. Name a number between 10 and 20 that has exactly 4 factors.