2. Number Theory GONE WILD!
Fun and Games
Number Theory GONE WILD!
Factors “Fall” into Families
Multiples Multiply like Rabbits!

3. What am I Learning Today?
Divisibility Rules
How will I show that I learned it?
Create a graphic organizer that contains the divisibility rule, an example and an explanation.
Use divisibility rules to determine the characteristics of numbers.

4. Then, try to identify “What’s the rule?”
Turn to a partner and try to figure out what the “yes” numbers have in common
YES NO
YES NO
Then, try to identify “What’s the rule?”

5. 48 is divisible by both 2 and 3
Divisibility Rules
A number is divisible by. . .
Example
Explanation
2 if the last digit is even (0, 2, 4, 6, or 8).
3,978
8 is even
3 if the sum of the digits is divisible by 3.
315
= 9
9 is divisible by 3
4 if the last two digits form a number divisible by 4.
8,512
12 is divisible by 4
5 if the last digit is 0 or 5.
14,975
The last digit is 5
6 if the number is divisible by both 2 and 3 48
48 is divisible by both 2 and 3
9 if the sum of the digits is divisible by 9.
711
= 9
9 is divisible by 9
10 if the last digit is 0.
15,990
The last digit is 0

6. Checking Divisibility
Tell whether 462 is divisible by 2, 3, 4, and 5. 2 3 4 5
The last digit, 2, is even.
Divisible
The sum of the digits is = is divisible by 3.
Divisible
The last two digits form the number is not divisible by 4.
Not divisible
Not divisible
The last digit is 2.
So 462 is divisible by 2 and 3.

7. Checking Divisibility
Tell whether 540 is divisible by 6, 9, and 10. 6 9 10
The number is divisible by both 2 and 3.
Divisible
The sum of the digits is = is divisible by 9.
Divisible
The last digit is 0.
Divisible
So 540 is divisible by 6, 9, and 10.

8. Turn to a partner and discuss the following:
Paired Discussion
Turn to a partner and discuss the following:
How can the divisibility rules help you identify composite numbers?
If a number is divisible by 4 and 9, by what other numbers is it divisible? Explain.