This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses interesting facts about diving whole numbers. By the end of the module students should be able to recognize a whole number that is divisible by 2, 3, 4, 5, 6, 8, 9, or 10.
Section overview
- Division by 2, 3, 4, and 5
- Division by 6, 8, 9, and 10
Quite often, we are able to determine if a whole number is divisible by another whole number just by observing some simple facts about the number. Some of these facts are listed in this section.
Division by 2, 3, 4, and 5
Division by 2
A whole number is
divisible by 2 if its
last digit is 0, 2, 4, 6, or 8.
The numbers 80, 112, 64, 326, and 1,008 are all divisible by 2 since the last digit of each is 0, 2, 4, 6, or 8, respectively.
The numbers 85 and 731 are
not divisible by 2.
Division by 3
A whole number is
divisible by 3 if the
sum of its digits is divisible by 3.
The number 432 is divisible by 3 since
$4+3+2=9$ and 9 is divisible by 3.
$\text{432}\xf73=\text{144}$
The number 25 is
not divisible by 3 since
$2+5=7$ , and 7 is not divisible by 3.
Division by 4
A whole number is
divisible by 4 if its
last two digits form a number that is divisible by 4.
The number 31,048 is divisible by 4 since the last two digits, 4 and 8, form a number, 48, that is divisible by 4.
$\text{31048}\xf74=\text{7262}$
The number 137 is not divisible by 4 since 37 is not divisible by 4.
Division by 5
A whole number is
divisible by 5 if its
last digit is 0 or 5.
Sample set a
Practice set a
State which of the following whole numbers are divisible by 2, 3, 4, or 5. A number may be divisible by more than one number.
Division by 6, 8, 9, 10
Division by 6
A number is
divisible by 6 if it is divisible by
both 2 and 3.
The number 234 is divisible by 2 since its last digit is 4. It is also divisible by 3 since
$2+3+4=9$ and 9 is divisible by 3. Therefore, 234 is divisible by 6.
The number 6,532 is
not divisible by 6. Although its last digit is 2, making it divisible by 2, the sum of its digits,
$6+5+3+2=\text{16}$ , and 16 is not divisible by 3.
Division by 8
A whole number is
divisible by 8 if its
last three digits form a number that is divisible by 8.
The number 4,000 is divisible by 8 since 000 is divisible by 8.
The number 13,128 is divisible by 8 since 128 is divisible by 8.
The number 1,170 is
not divisible by 8 since 170 is not divisible by 8.
Division by 9
A whole number is
divisible by 9 if the
sum of its digits is divisible by 9.
The number 702 is divisible by 9 since
$7+0+2$ is divisible by 9.
The number 6588 is divisible by 9 since
$6+5+8+8=\text{27}$ is divisible by 9.
The number 14,123 is
not divisible by 9 since
$1+4+1+2+3=\text{11}$ is not divisible by 9.
Division by 10
A Whole number is
divisible by 10 if its
last digit is 0.
Sample set b
Practice set b
State which of the following whole numbers are divisible 6, 8, 9, or 10. Some numbers may be divisible by more than one number.
Exercises
For the following 30 problems, specify if the whole number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10. Write "none" if the number is not divisible by any digit other than 1. Some numbers may be divisible by more than one number.
Exercises for review