Download Divisibility Rules

Divisibility Rules
Number
2
3
Rule
If the number is even then it is divisible by 2 . All
numbers ending in 0, 2, 4, 6, or 8 are divisible by 2.
Find the sum of all the digits in the number. If the sum is
divisible by 3 then the number is divisible by 3
4
If the last two digits of the number are divisible by 4 then
the number is divisible by 4
5
If the number ends in 0 or 5 then the number is divisible
by 5
If the number is divisible by 3 and it is an even number
then it is divisible by 6
6
7
7
8
9
First Rule
Take the last digit in the number and double it then
subtract that number from the rest of the digits in the
number. If that number is divisible by 7 then the entire
number is divisible by 7
Second Rule
Take the number and beginning on the right hand side,
multiply each digit by 1, 3, 2, 6, 4, 5. Repeat the
sequence as necessary. Add the products. If the sum is
divisible by 7 then the number is divisible by 7.
If the last three digits in the number are divisible by 8
then the number is divisible by 8
Find the sum of all the digits in the number. If the sum is
divisible by 9 then the number is divisible by 9
Example(s)
2, 358, 2000 These numbers are even so
they are divisible by 2.
2565 2 + 5 + 6 + 5 = 18
18 is divisible by 3 so 2565 is divisible by
3
285716 The last two digits are 16.
16 is divisible by 4 so 285716 is divisible
by 4
2750 ends in 0, so it is divisible by 5
765 ends in 5, so it is divisible by 5
2742 is an even number and the sum of its
digits is 15 which is divisible by 3, so this
number is divisible by 6
546
6 x 2 = 12.
54 – 12 = 42
42 is divisible by 7, so 546 is divisible by 7
1834
4(1) + 3(3) + 8(2) + 1(6) = 35
35 is divisible by 7 so 1834 is divisible by
7.
3024 The last three digits are 024. 024
is divisible by 8 so 3024 is divisible by 8.
2565 2 + 5 + 6 + 5 = 18
18 is divisible by 9 so 2565 is divisible
by 9
10
If the number ends in 0 then it is divisible by 10
11
Add up the alternate digits of a number then add up the
other set of alternate digits. If the sums of the alternate
digits equal each other then the whole number is
divisible by 11. Also, if the difference of the alternate
digits is 11 or a multiple of 11, then the whole number id
divisible by 11.
3080 ends in 0 so the number is divisible
by 10.
123,456,322
1 + 3 + 5 + 3 + 2 = 14 and
2 + 4 + 6 + 2 = 14
Since the sums are equal to each other
the number is divisible by 11.