Test of Divisibility
1. Divisibility By 2:
A number is divisible by 2, If its unit digit is any of 0, 2, 4, 6, 8
Ex: 876456 is
divisible by 2, while 987345 is not.
2. Divisibility by 3:
A number is divisible by 3, If the sum of its digits is divisible by 3 or If
the sum of the digits is equal to 3, 6, 9.
Ex: 592482 is divisible
by 3, since the sum of the digits is 3.
3. Divisible by 4: A
number is divisible by 4, if the number formed by last two digits of the number
is divisible by 4.
Ex: 892648 is
divisible by 4, since the last two digits are divisible by 4.
4. Divisible by 5: A
number is divisible by 5, if its unit’s digit either 5 or 0.
Ex: 87654560 is
divisible by 5, since the last digit is 0.
5. Divisible by 6: A
number is divisible by 6, if following conditions satisfies.
a.
The number should be even.
b.
The sum of all digits should be divisible by 3.
Ex: 35256 is divisible
by 6, since it is even and the sum is divisible by 3.
6. Divisible by 8: A
number is divisible by 8, if the number formed by the last three digits of the
number is divisible by 8.
Ex: 953360 is
divisible by 8, since last three digits (360) is divisible by 8.
7. Divisible by 9: A
number is divisible by 9, if the sum of the digits is equal to 9.
Ex: 99999 is
divisible by 9, since the sum of digits is equal to 9.
8. Divisible by 10: A
number is divisible by 10, if its unit digit is 0.
Ex: 123450 is
divisible by 10, since its unit digit is 0.
9. Divisible by 11: A
number is divisible by 11, If the difference of the sum of its digits at odd
places and the sum of even places, is either 0 or a number divisible by 11.
Ex: 999999 is
divisible by 11, since the difference of the sum of its digits at odd places
and the sum of even places is 0.
10. Divisible by 12: A
number is divisible by 12, If it divisible by both 3 and 4.
