TESTS OF DIVISIBILITY[ Chapter #1]
1. Divisibility By 2:
A number is divisible by 2 if its unit digit is any of [0,2,4,6,8]
Example:
- 3468 is divisible by 2 while 86945 is not divisible by 2
2. Divisibility By 3:
A number is divisible by 3 only when the sum of its digits is divisible by 3.
Example:
- In the number 345, the sum of digits[3+4+5=12] which is divisible by 3
- In the number 445, the sum of digits[4+4+5=13] which is not divisible by 3
3. Divisibility By 9:
A number is divisible by 9 only when the sum of its digits is divisible by 9.
Example:
- In the number 246591, the sum of digits[2+4+6+5+9+1=27] which is divisible by 9
4. Divisibility By 8:
A number is divisible by 8 if the number formed by hundred's ten's and unit's digit of the given number is divisible by 8.
Example:
- In the number 16789352, the number formed by last 3 digits namely 352 is divisible by 8.
So 16789352 is divisible by 8.
5. Divisibility By 10:
A number is divisible by 10 only when its unit digit is 0
Example:
5. Divisibility By 10:
A number is divisible by 10 only when its unit digit is 0
Example:
- 7560 is divisible by 10 since its unit digit is 0
- 67805 is not divisible by 10 since its unit digit is 5
6. Divisibility By 5:
A number is divisible by 5 only when its unit digit is 0 or 5.
Example:
- 58595 and 30055 is divisible by 5
7. Divisibility By 4:
A number is divisible by 4 is the sum of its last two digits is divisible by 4.
Example:
- 6879376 is divisible by 4 since 76 is divisible by 4
8. Divisibility By 11:
A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or a number divisible by 11.
Example: