Download Divisibility Rules

Divisibility Rules
Divisibility Rules allow us to determine if one number divides evenly into another number with out going
through a formal long division process. A quick mental calculation is often employed with divisibility rules so
that they become a time saving device that eliminates the need for formal long division. Although divisibility
rules can be developed for any divisor, we only study those divisors that are in frequent use in the
developmental mathematics classroom
For divisibility by :
2
3
4
5
6
8
9
10
Most Frequently Used Divisibility Rules
(Short Version)
Check to see if…
Last digit is a 0, 2, 4, 6, or 8. (This means the number is even.)
Sum of the digits is divisible by 3.
The number formed by the last two digits is divisible by 4.
Last digit is either a 0 or 5.
The number is divisible by BOTH 2 AND 3.
The number formed by the last three digits is divisible by 8.
Sum of the digits is divisible by 9.
Last digit is a 0.
Divisibility rules can also be stated as conditional (if–then) statements in a much longer form than as stated
above. Below is an alternate (but equivalent) version of the same information.
Most Frequently Used Divisibility Rules
(Long Version)
Divisibility Condition :
Example
A number is divisible by 2 if the last digit is a 0,
2, 4, 6, or 8. (Also, if the number is even.)
A number is divisible by 3 if the sum of the digits
is divisible by 3.
A number is divisible by 4 if the number formed
by the last two digits is divisible by 4.
A number is divisible by 5 if the last digit is either
a 0 or 5.
A number is divisible by 6 if it is divisible by
BOTH 2 AND 3.
A number is divisible by 8 if the number formed
by the last three digits is divisible by 8.
A number is divisible by 9 if the sum of the digits
is divisible by 9.
A number is divisible by 10 if the last digit is a 0.
1256 is divisible by 2 since the last digit is 6.
1587 is divisible by 3 since the sum of the digits
is 21 (1+5+8+7 = 21), and 21 is divisible by 3.
512 is divisible by 4 since the number formed
by the last two digits is 12, and 12 is divisible
by 4.
895 is divisible by 5 since the last digit is a 5.
462 is divisible by 6 since it is divisible by
BOTH 2 (it’s even) AND 3 (since 4+6+2 = 12.)
56160 is divisible by 8 since the number formed
by the last three digits is 160, and 160 is
divisible by 8.
7515 is divisible by 9 since the sum of the digits
is 18 (7+5+1+5 = 18), and 18 is divisible by 9.
6320 is divisible by 10 since the last digit is 0.