Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Search
MENU
Learning Math Home
Number and Operations Session 5, Part B: Divisibility Tests
 
Session5 Part A Part B Part C Homework
 
Glossary
number Site Map
Session 5 Materials:
Notes
Solutions
Video

Session 5, Part B:
Divisibility Tests

In This Part: Developing Testing Rules | Divisibility Tests for 2, 5, and 10
Divisibility Tests for 3 and 9 | Divisibility Tests for 4 and 8 | Divisibility Test for 11

As you've seen, it is easy to tell if a counting number is divisible by 2, 5, or 10 -- just look at the units digit:

Row

Numbers

1

1

11

21

31

151

2461

2

2

12

22

32

152

2462

3

3

13

23

33

153

2463

4

4

14

24

34

154

2464

5

5

15

25

35

155

2465

6

6

16

26

36

156

2466

7

7

17

27

37

157

2467

8

8

18

28

38

158

2468

9

9

19

29

39

159

2469

10

10

20

30

40

160

2470

Blue: Divisible by 2, but not 5 or 10
Red: Divisible by 5, but not 2 or 10
Green: Divisible by 2, 5, and 10

Since 2, 5, and 10 all divide 10 evenly, the divisibility tests for 2, 5 and 10 are similar in that you only have to examine the units digit. If the units digit is 0, then 10 divides the number. If the units digit is 0 or 5, then 5 divides the number. If the units digit is even (0, 2, 4, 6, or 8), then 2 divides the number.

Why does this work? Any multi-digit number can be written as a sum by replacing the units digit with a 0 and adding the original units digit. For example, the five-digit number 12,345 can be written as 12,340 + 5, where 5 is the units digit of the number. The idea that abcde = abcd0 + e can be extended to any number of digits.

The number abcd0 is 10 • abcd, so 2, 5, and 10 all divide the number abcd0. So if the units digit is 0, then 10 divides the number. If the units digit is not 0, then 10 does not divide the number. Similarly, you only need to check the units digit for divisibility by 2 or 5.


Next > Part B (Continued): Divisibility Tests for 3 and 9

Learning Math Home | Number Home | Glossary | Map | ©

Session 5: Index | Notes | Solutions | Video

Home | Catalog | About Us | Search | Contact Us | Site Map

  • Follow The Annenberg Learner on Facebook

© Annenberg Foundation 2013. All rights reserved. Privacy Policy