Rule
Of Divisibility
1. Every number is divisible by 1.
Example: 7 ÷ 1 = 7
2. Divisibility
by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
Example: 14 ÷ 2 = 7
3. Divisibility
by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
Example: 123 (1 + 2 + 3 = 6, and 6 ÷ 3 = 2)
4. Divisibility
by 4: A number is divisible by 4 if the last two digits form a number that is
divisible by 4.
Example: 124 (24 is divisible by 4)
5.
Divisibility
by 5: A number is divisible by 5 if its last digit is 0 or 5.
Example: 85 ÷ 5 = 17
6. Divisibility
by 6: A number is divisible by 6 if it is divisible by both 2 and 3.
Example: 54 (last digit is even, and 5 + 4 = 9,
which is divisible by 3)
7. Divisibility
by 7: A number is divisible by 7 if doubling the last digit and subtracting it
from the rest of the number results in a number that is divisible by 7.
Example: 203 (Double 3 is 6; 20 - 6 = 14, which is
divisible by 7)
8. Divisibility
by 8: A number is divisible by 8 if the last three digits form a number that is
divisible by 8.
Example: 1,000 (000 is divisible by 8)
9. Divisibility
by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
Example: 729 (7 + 2 + 9 = 18, and 18 ÷ 9 = 2)
10. Divisibility by 10: A number is divisible by 10 if
its last digit is 0.
Example: 120 ÷ 10 = 12
11. Divisibility
by 11: A number is divisible by 11 if the difference between the sum of the
digits in odd positions and the sum of the digits in even positions is either 0
or divisible by 11.
Example: 121 (1 - 2 + 1 = 0, which is divisible by
11)
12. Divisibility by 12: A number is divisible by 12 if
it is divisible by both 3 and 4.
Example: 36 (Sum of digits 3 + 6 = 9, which is
divisible by 3 and last two digits 36 is divisible by 4)
13. Divisibility by 13: A number is divisible by 13 if
subtracting 9 times the last digit from the rest of the number results in a
number that is divisible by 13.
Example: 169 (Double 9 is 18; 16 - 18 = -2, which
is divisible by 13)
14. Divisibility by 14: A number is divisible by 14 if
it is divisible by both 2 and 7.
Example: 98 (Last digit is even, and 98 ÷ 7 = 14)
15. Divisibility by 15: A number is divisible by 15 if
it is divisible by both 3 and 5.
Example: 45 (Sum of digits 4 + 5 = 9, which is
divisible by 3 and last digit is 5)
