Divisibility Tests for 3 and 9

New York State Common Core Math Grade 6, Module 2, Lesson 17
Grade 6, Module 2, Lesson 17 Worksheet & Solutions

Lesson 17 Student Outcomes

• Students apply divisibility rules, specifically for 3 and 9, to understand factors and multiples.

Opening Exercise

Below is a list of numbers. Place each number in the circle(s) that is a factor of the number. You will place some numbers more than once.

Divisibility Rules

• Divisibility rule for 2: If and only if its last digit is 0, 2, 4, 6, or 8.
• Divisibility rule for 3: If the sum of the digits is divisible by 3.
• Divisibility rule for 4: If and only if its last two digits are a number divisible by 4.
• Divisibility rules for 5: If and only if its last digit is 0 or 5.
• Divisibility rule for 8: If and only if its last three digits are a number divisible by 8.
• Divisibility rule for 9: If the sum of the digits is divisible by 9.
• Divisibility rule for 10: If and only if its last digit is 0.

Example 1

Is 378 divisible by 3 or 9? Why or why not?
a. What are the three digits in the number 378?
b. What is the sum of the three digits?
c. Is 18 divisible by 9?
d. Is the entire number 378 divisible by 9? Why or why not?
e. Is the number 378 divisible by 3? Why or why not?

Example 2

Is 3,822 divisible by 3 or 9? Why or why not?

Exercises

Circle ALL the numbers that are factors of the given number. Complete any necessary work in the space provided.

Lesson Summary

To determine if a number is divisible by 3 or 9:

• Calculate the sum of the digits.
• If the sum of the digits is divisible by 3, the entire number is divisible by 3.
• If the sum of the digits is divisible by 9, the entire number is divisible by 9.

Note: If a number is divisible by 9, the number is also divisible by 3.

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Example 1 - Example 2

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Problem Set

1. Is 32,643 divisible by both 3 and 9? Why or why not?
2. Circle all the factors of 424,380 from the list below.
   2, 3, 4, 5, 8, 9, 10
3. Circle all the factors of 322,875 from the list below.
   2, 3, 4, 5, 8, 9, 10
4. Write a 3-digit number that is divisible by both 3 and 4. Explain how you know this number is divisible by 3 and 4.
5. Write a 4-digit number that is divisible by both 5 and 9. Explain how you know this number is divisible by 5 and 9.

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