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Learning Math Home
Number and Operations Session 5, Part B: Divisibility Tests
 
Session5 Part A Part B Part C Homework
 
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Session 5 Materials:
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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

You probably used the test for 2 and the test for 3 to check divisibility by 6. We cannot, however, use the test for 2 twice to check for divisibility by 4. Using 2 and 3 works because they are relatively prime; that is, the only factor they have in common is 1.

The test for divisibility by 2 can be modified for testing divisibility by 4 and 8. Here's how it works.

Since 4 does not divide 10, but 4 does divide 100, rewrite the number, such as the five-digit number abcde, into two parts, abc00 + de; this is 100 times the three-digit number abc plus the two-digit number de. Since 4 divides 100, then 4 divides abc00, and all that needs to be checked is the two-digit number de. If de is divisible by 4, then the entire number is divisible by 4.

For example, to check whether the number 23,456 is divisible by 4, rewrite the number as 23,400 + 56. We know that 4 divides 23,400. Since 4 also divides 56, then 4 divides 23,456.

The test for divisibility by 8 continues this pattern. Because 8 does not evenly divide either 10 or 100, but it does divide 1,000, separate the number -- for example, separate abcde into two parts, ab000 + cde. To test 23,456, write the numbers 23,000 + 456. Since 8 divides 23,000 and 8 divides 456, then 8 evenly divides 23,456.

You can try these tests with the numbers in the chart below:

Row

Numbers

1

1

11

21

31

151

2461

10,561

2

2

12

22

32

152

2462

10,562

3

3

13

23

33

153

2463

10,563

4

4

14

24

34

154

2464

10,564

5

5

15

25

35

155

2465

10,565

6

6

16

26

36

156

2466

10,566

7

7

17

27

37

157

2467

10,567

8

8

18

28

38

158

2468

10,568

9

9

19

29

39

159

2469

10,569

10

10

20

30

40

160

2470

10,570

Blue: Divisible by 4, but not 8
Red: Divisible by 4 and 8


 

Problem B5

Solution  

Use the divisibility test to determine whether the following numbers are divisible by 4 and 8:

a. 

32,464

b. 

82,426



video thumbnail
 

Video Segment
In this video segment, Rhonda and Andrea explain how they found the test for divisibility by 4. They then extend the same reasoning to discover the divisibility test for 8 and other powers of 2.

If you are using a VCR, you can find this segment on the session video approximately 9 minutes and 31 seconds after the Annenberg Media logo.

 

Next > Part B (Continued): Divisibility Test for 11

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