Divisibility
This is a complete lesson with explanations and exercises about the concept of divisibility, and about factors, divisors, and multiples, meant for fourth grade math. The lesson also reviews the divisibility rules for 2, and 5, and 10.
A number a is divisible by another number
b if the division
a ÷
b is exact (no remainder).
For example, 18 ÷ 3 = 6. So, 18 is divisible by 3. Also, 18 is divisible by 6, because we can write the other division 18 ÷ 6 = 3. So, 18 is divisible by both 6 and 3. We say 6 and 3 are divisors or factors of 18. 


1. Divide and determine if the numbers are divisible by the given number.
a. 21 ÷ 3 = ______ Is 21 divisible by 3?

b. 40 ÷ 6 = _______ Is 40 divisible by 6? 
c. 84 ÷ 7 = _______ Is 7 a factor of 84? 
2. Answer the questions. You may need long division.
a. Is 98 divisible by 4?

b. Is 603 divisible by 7?

c. Is 3 a factor of 1,256?

called factors and the result is called a product. So, since 6 × 7 = 42, 6 and 7 are factors of 42. From this multiplication fact we
can write two divisions:
42 ÷ 6 = 7 and 42 ÷ 7 = 6. 

Yet one more new word that ties in with all of this: multiple. We say 42 is a multiple of 6, because 42 is some number times 6, namely 7 × 6. And of course 42 is also a multiple of 7, because it is some number times 7! 
3. Fill in.
Here's a
multiplication fact: 8 × 9 = 72. So, 8 is a ____________________ of 72,
and so is 9. Also, 72 is a ____________________ of 8, and also 72 is
a ____________________ of 9. And, 72 is ____________________ by 8
and also by 9.
4. Fill in.
a. Is 5 a factor of 55? Yes, because ____ × ____ = ________. 
b. Is 8 a divisor of 45? No, because ____ ÷ ____ = _________. 
c. Is 36 a multiple of 6? ____, because ____ × ____ = ______. 
d. Is 34 a multiple of 7? _____, because ____ ÷ ____ = _______. 
e. Is 7 a factor of 46? ____, because __________________. 
f. Is 63 a multiple of 9? ____, because _________________. 
Multiples of 6 are all
those numbers we get when we multiply 6 by other numbers.
In fact, the skipcounting pattern of 6 gives us a list of multiples of 6: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, and so on. 
5. a. Make a list of multiples of 11, starting at 0 and at least till 154.
b. Make a list of multiples of 111, starting at 0. Make it as long as you can in this space!
Divisibility by 2 Numbers that are
divisible by 2 are called even numbers. Even numbers end in 0, 2, 4, 6, or 8. Every second number is even. 
Divisibility by 5 Numbers that end in 0 and 5 are divisible by 5. For example, 10, 35, 720, and 3,675 are such numbers. 
6. Mark with “x” if the numbers are divisible by 2 or 5.



Divisibility by 10 Numbers that end in 0 are divisible by 10. For example, 10, 60, 340, and 2,570 are such numbers. 
7. Mark an “x” if the numbers are divisible by 2 or 5 or 10.



If a number is divisible by 10, it ends in zero, so it is ALSO divisible by ____ and ____. 
8. a. Write a list of numbers divisible by 2, from 0 to 60.
_____________________________________________________________
This is also a list of ______________________________ of 2.
b. In the list above, underline those
numbers that are divisible by 4.
What do you notice?
c. In the list above, color those numbers
that are divisible by 6.
What do you notice?
d.
Which numbers are divisible by both 4 and 6?
9. a. Write a list of numbers divisible by 3, from 0 to 60.
_____________________________________________________________
This is also a list of ______________________________ of 3.
b. In the list above, underline those
numbers that are divisible by 6.
What do you notice?
c. In the list above, color
those numbers that are divisible by 9.
What do you notice?
10. Use the lists you made in (7) and (8). Find numbers
that are divisible by both 2 and 9.
11. What number is a factor of every number?
12. Twenty is a multiple of 4. It is also a multiple of
5. It is also a multiple of four
other numbers. Which ones?
Who am I? Divided by 9, I leave a remainder of 6. 
Who am I? I am a multiple of 3, 4, 5, and 6. 
This lesson is taken from my book Math Mammoth Division 2. The lesson addresses the following Common Core standards for 4th grade: 4.OA.4.
Math Mammoth Division 2
A selfteaching worktext for 4th grade that covers long division, finding fractional parts with division, word problems, remainder, average, and divisibility.
Download ($5.10). Also available as a printed copy.