1. Discovering
Divisibility Rules

2. These numbers are all divisible by 2. Can you see why?4 18
912
636
9,720
Here’s a hint --
The ones digit is even!

3. A number is divisible by 2 if the ones digit is even.
Are these numbers divisible by 2? 5 82
917
5,276
8,478,184 NO
YES NO
YES
YES

4. These numbers are all divisible by 3. Can you see why?
Here’s a hint –
**Add up the digits of each number** 9 63
714
225
9,720
The sum of the digits is divisible by 3!

5. A number is divisible by 3 if the sum of the digits is divisible by 3.
Are these numbers divisible by 3? 7 27
824
271,360
9,265,689 NO
YES NO NO
YES

6. These numbers are all divisible by 4. Can you see why?16
912
720
8,224
917,532
Here’s a hint --
If the last two digits form a number divisible by 4!

7. Are these numbers divisible by 4?
A number is divisible by 4 if the last two digits form a number divisible by 4.
Are these numbers divisible by 4? 15
240
1,693
4,408
12,982,540 NO
YES NO
YES
YES

8. These numbers are all divisible by 5. Can you see why?15
280
2,475
82,470
153,645
Here’s a hint --
The ones digit is a 0 or 5!

9. A number is divisible by 5 if the ones digit is a 0 or 5.
Are these numbers divisible by 5? 15
240
1,693
4,408
12,982,540
YES
YES NO NO
YES

10. These numbers are all divisible by 6. Can you see why?
Here’s a hint –
**Think about our other rules and what two numbers are factors of 6.** 48 90
174
1,044
39,720
The number is divisible by both 2 and 3!

11. A number is divisible by 6 if the number is divisible by both 2 and 3.
Are these numbers divisible by 6?
135
462
7,026
50,319
12,982,440 NO
YES
YES NO
YES

12. These numbers are all divisible by 9. Can you see why?
Here’s a hint –
**Add up the digits of each number** 18
612
7,443
81,225
99,720
The sum of the digits is divisible by 9!

13. A number is divisible by 9 if the sum of the digits is divisible by 9.
Are these numbers divisible by 9? 72
183
1,287
189,101
12,982,440
YES NO
YES NO NO

14. These numbers are all divisible by 10. Can you see why?50
240
8,770
42,420
153,640
Here’s a hint --
The ones digit is 0!

15. A number is divisible by 10 if the ones digit is 0.
Are these numbers divisible by 10? 70
183
1,280
189,101
142,982,530
YES NO
YES NO
YES

16. Determine whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10.
712
2, 4
1,035
3, 5, 9
32,221
none
8,340
2, 3, 4, 5, 6, 10

17. Assignment
Divisibility Rules WS
You can do it!