# 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.