1. Divisibility
Rules!

2. What is Divisibility? Divisibility means that :
after dividing, there will be no remainders. 3 1 30
6 2 2
6 1 2 6 6 2 1 2
No reminders 1
Reminders

3. Use your calculator
÷ 4 =
542 ÷ 2 =
59 ÷ 3=
620 ÷ 5 =
75 ÷ 4 =
12040 ÷ 10 =

4. The divisibility rules can help you!
356,821
 Can you tell by just looking at this number if it is divisible by 2?
by 5?
by 10?
by 3 ?
by 9?
By 6?
The divisibility rules can help you!

5. Divisibility rules help you learn shortcuts to tell when a number can be divided by another number without any remainders.

6. Divisibility by 2

7. Divisibility by 2 18 ÷ 2 = 9 22 ÷ 2 = 11 A number is divisible by 2
if the number is even.
18 ÷ 2 = 9
22 ÷ 2 = 11
(18 and 22: Notice that both of these dividends are even.)
21 ÷ 2 = 10 R1
(21: not an even number.)

8. Are these numbers divisible by 2?
On your whiteboard
Are these numbers divisible by 2?
127 24
4678 11
325 20

9. Divisibility by 5

10. Divisibility by 5
A number is divisible by 5 if it ends in 0 or 5.
25 ÷ 5 = 5
23 ÷ 5 = 4 R3

11. Are these numbers divisible by 5?
(Units are not 0 or 5
328
215
4670 21 84 9
185470
(Units are not 0 or 5
(Units are not 0 or 5
(Units are not 0 or 5

12. Divisibility by 10

13. Divisibility by 30 ÷ 10 = 3 340 ÷ 10 = 34 67 ÷ 10 = 6 R7
A number is divisible by 10 if it ends in 0.
30 ÷ 10 = 3
340 ÷ 10 = 34
67 ÷ 10 = 6 R7
784 ÷ 10 =78 R4

14. Divisibility By: 2 5 10
1825
346
510
1108

15. Complete your worksheet

16. Divisibility by 3 Is the number 135 divisible by 3?
A number is divisible by 3 if the sum of the digits is divisible by 3.
Is the number 135 divisible by 3?
Add the digits: = 9
Yes, 135 is divisible by 3 because the sum of the digits is divisible by 3.

17. Are these numbers divisible by 3?
328
216
4680 21 85 19
65410

18. Divisibility by 6 A number is divisible by 6
if it is divisible by both 2 and 3.
Is 42 divisible by 6?
Think:
Is 42 divisible by 2?
Is 42 divisible by 3?
Is 51 divisible by 6?

19. Are these numbers divisible by 6?32 21 48 36 85 18
65410

20. Divisibility by 6

21. Divisibility by 9 369 is divisible by 9 because 3 + 6 + 9 =18
A number is divisible by 9 if the sum of its digits is divisible by 9.
369 is divisible by 9
because
=18
1 + 8 = 9
and
9 is divisible by 9.

22. Are these numbers divisible by 9?42
207 61
1288 33 24
65410

23. Divisibility by 9

24. A number is divisible by 100 if the last two digits are 00
Divisibility by 25
Divisibility by 100
A number is divisible by 25 if the last two digits are 25 , 75 , 50 , 00
A number is divisible by 100 if the last two digits are 00
Examples
Examples
1420
1420 ÷ 25 =56.8
600
600 ÷ 25 = 24
6500
6500÷ 100=65
610
610÷ 100= 6.1

25. Divisibility by 4
A number is divisible by 4 if the last two digits are divisible by 4.
Examples:
÷ 4 = 5
÷ 4 = 18

26. Divisibility by 4

27. Now You Try:
Which number IS NOT divisible by 4?

29. Complete your worksheet

30. WONDERFUL

31. The last 2 digits are divisible by 4.