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,


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

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. 
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 ___ 
41 ÷ 5 = ___, R ___ 
51 ÷ 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 selfteaching 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.