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Divisibility

This is a complete lesson with explanations and exercises about the concept of divisibility, for third grade. If a division is exact (there is no remainder), then we say a number is divisible by another. This lesson also lets students explore the concept of divisibility by 3, 5, and 10, and see the patterns in the division tables.



If there is no remainder, we say division is exact. For example,

18 ÷ 9 = 2, the remainder is 0.

We say:  18 is divisible by 9.

24 ÷ 4 = 6, R 0.

24 is divisible by 4.

33 ÷ 11 = 3, R 0.

33 is divisible by 11.

If there is a remainder, we say division is not exact. For example,

15 ÷ 4 = 3, remainder 3.

15 is NOT divisible by 4.

17 ÷ 7 = 2, R 3.

17 is not divisible by 7.

20 ÷ 3 = ___, R ___ .

20 is not divisible by 3.

1.  Follow the example and find if the following numbers are divisible by given numbers.

a.  Is 15 divisible by 5?

Yes, because  15 ÷ 5 = 3, R 0.

b.  Is 22 divisible by 2?

Yes/no, because 

c.  Is 17 divisible by 5?

No, because 17 ÷ 5 = 3, R 2.
There is a remainder. 

d.  Is 14 divisible by 3?

Yes/no, because 

e.  Is 24 divisible by 5?

Yes/no, because

f.  Is 30 divisible by 5?

Yes/no, because

g.  Is 17 divisible by 3?

 

h.  Is 27 divisible by 3?

i.  Is 14 divisible by 2?

 

j.  Is 48 divisible by 12?

 


2. If the division is exact, mark the remainder as 0.

1 ÷ 3 = 0, R 1

2 ÷ 3 = 0, R 2

3 ÷ 3 = ___, R ___

4 ÷ 3 = ___, R ___

5 ÷ 3 = ___, R ___

6 ÷ 3 = ___, R ___

7 ÷ 3 = ___, R ___

8 ÷ 3 = ___, R ___

9 ÷ 3 = ___, R ___

10 ÷ 3 = ___, R ___

11 ÷ 3 = ___, R ___

12 ÷ 3 = ___, R ___

13 ÷ 3 = ___, R ___

14 ÷ 3 = ___, R ___

15 ÷ 3 = ___, R ___

16 ÷ 3 = ___, R ___

17 ÷ 3 = ___, R ___

18 ÷ 3 = ___, R ___

19 ÷ 3 = ___, R ___

20 ÷ 3 = ___, R ___

21 ÷ 3 = ___, R ___

22 ÷ 3 = ___, R ___

23 ÷ 3 = ___, R ___

24 ÷ 3 = ___, R ___

25 ÷ 3 = ___, R ___

26 ÷ 3 = ___, R ___

27 ÷ 3 = ___, R ___

Numbers that were divisible by 3: ___________________________________

Where have you seen that list before?

 

31 ÷ 5 = ___, R ___
32 ÷ 5 = ___, R ___
33 ÷ 5 = ___, R ___
34 ÷ 5 = ___, R ___
35 ÷ 5 = ___, R ___
36 ÷ 5 = ___, R ___
37 ÷ 5 = ___, R ___
38 ÷ 5 = ___, R ___
39 ÷ 5 = ___, R ___
40 ÷ 5 = ___, R ___

41 ÷ 5 = ___, R ___
42 ÷ 5 = ___, R ___
43 ÷ 5 = ___, R ___
44 ÷ 5 = ___, R ___
45 ÷ 5 = ___, R ___
46 ÷ 5 = ___, R ___
47 ÷ 5 = ___, R ___
48 ÷ 5 = ___, R ___
49 ÷ 5 = ___, R ___
50 ÷ 5 = ___, R ___

51 ÷ 5 = ___, R ___
52 ÷ 5 = ___, R ___
53 ÷ 5 = ___, R ___
54 ÷ 5 = ___, R ___
55 ÷ 5 = ___, R ___
56 ÷ 5 = ___, R ___
57 ÷ 5 = ___, R ___
58 ÷ 5 = ___, R ___
59 ÷ 5 = ___, R ___
60 ÷ 5 = ___, R ___

Numbers that were divisible by 5: ___________________________________

Where have you seen that list before?



3. a. Write a list of twelve different numbers that are divisible by 6.
 

     b. Then write twelve different numbers that are NOT divisible by 6.

 

4. Divide by 10! Discuss with your teacher the patterns you notice.

0 ÷ 10 = 0, R __

1 ÷ 10 = 0, R 1

2 ÷ 10 = 0, R 2

3 ÷ 10 = ___, R ___

4 ÷ 10 = ___, R ___

5 ÷ 10 = ___, R ___

6 ÷ 10 = ___, R ___

7 ÷ 10 = ___, R ___

8 ÷ 10 = ___, R ___

9 ÷ 10 = ___, R ___

10 ÷ 10 = ___, R ___

11 ÷ 10 = ___, R ___

12 ÷ 10 = ___, R ___

13 ÷ 10 = ___, R ___

14 ÷ 10 = ___, R ___

15 ÷ 10 = ___, R ___

16 ÷ 10 = ___, R ___

17 ÷ 10 = ___, R ___

18 ÷ 10 = ___, R ___

19 ÷ 10 = ___, R ___

20 ÷ 10 = ___, R ___

21 ÷ 10 = ___, R ___

22 ÷ 10 = ___, R ___

23 ÷ 10 = ___, R ___

24 ÷ 10 = ___, R ___

25 ÷ 10 = ___, R ___

26 ÷ 10 = ___, R ___

27 ÷ 10 = ___, R ___

28 ÷ 10 = ___, R ___

29 ÷ 10 = ___, R ___

Make a list of numbers less than 150 that are divisible by 10:

__________________________________________________

5. Did you notice the pattern of reminders in the previous exercise?  Based on that
     you can easily solve these:

a. b. c.

41 ÷ 10 = ____, R ___

56 ÷ 10 = ____, R ___

92 ÷ 10 = ____, R ___

60 ÷ 10 = ____, R ___

77 ÷ 10 = ____, R ___

41 ÷ 10 = ____, R ___

80 ÷ 10 = ____, R ___

53 ÷ 10 = ____, R ___

99 ÷ 10 = ____, R ___

100 ÷ 10 = ____, R ___

101 ÷ 10 = ____, R ___

122 ÷ 10 = ____, R ___




This lesson is taken from Maria Miller's book Math Mammoth Division 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.


Math Mammoth Division 1

A self-teaching worktext for 3rd grade that covers division concept, division & multiplication fact families, word problems, division facts, remainder, zero and one in division, and more.Download ($3.70). Also available as a printed copy.

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