Divisibility Rules for 3, 6, and 9

Introduction

• Instructor: Teacher Pro
• Lesson Objective: Use the rules for divisibility by 3, 6, and 9 to find common factors
• Previous Lesson: Rules for divisibility by 2, 5, and 10

Divisibility Rules

1. Divisibility by 3:

   • A number is divisible by 3 if the sum of its digits is divisible by 3
   • Example: 27 (2 + 7 = 9, which is divisible by 3)

2. Divisibility by 6:

   • A number is divisible by 6 if it is divisible by both 2 and 3
   • Example: 144 is divisible by 2 (even number) and 3 (1 + 4 + 4 = 9, which is divisible by 3)

3. Divisibility by 9:

   • A number is divisible by 9 if the sum of its digits is divisible by 9
   • Example: 87651 (8 + 7 + 6 + 5 + 1 = 27, which is divisible by 9)

Learning Tasks

Learning Task 1

• Observe and apply divisibility rules
  1. Is 27 divisible by 3?
     • Yes, 2 + 7 = 9 (divisible by 3)
  2. Is 144 divisible by 6?
     • Yes, divisible by 2 (even) and 3 (sum of digits = 9)
  3. Is 87,651 divisible by 9?
     • Yes, 8 + 7 + 6 + 5 + 1 = 27 (divisible by 9)

Learning Task 2

• Table Exercise: Determine if given numbers are divisible by 2, 5, and 10
  1. 245: Divisible by 5
  2. 330: Divisible by 2, 5, 10
  3. 400: Divisible by 2, 5, 10
  4. 412: Divisible by 2
  5. 875: Divisible by 5

Learning Task 3

• Problem Solving: Hannah's Garden
  • 126 sunflower plants
  • Can be arranged in groups of 3, 6, and 9

Learning Task 4

• Classify Numbers: Check divisibility by 3, 6, 9, or none
  • Divisible by 3: 1128, 2235, 7134, 9120, 5661, 9999, 5004, 2088
  • Divisible by 6: 1128, 4020, 9120, 5004, 7134, 2088
  • Divisible by 9: 5004, 2088, 5661, 9999
  • Not Divisible by any: 5228, 1124, 21001, 1750, 6625, 3122, 4445, 7886, 9457

Key Points

• Divisibility by 3: Sum of digits divisible by 3
• Divisibility by 6: Divisible by both 2 and 3
• Divisibility by 9: Sum of digits divisible by 9 or a multiple of 9

Conclusion

• Summary of Divisibility Rules
• Farewell by Teacher Pro: Hope you learned a lot; see you next time!