Divisibility Rules

 Divisibility Rules

Divisibility rules - Divisibility rules are a set of guidelines that help to determine if one number is divisible by another without having to perform the actual division. Here are some of the most common divisibility rules:

1. Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8).
2. Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
3. Divisibility by 4: A number is divisible by 4 if the last two digits of the number are divisible by 4.
4. Divisibility by 5: A number is divisible by 5 if its last digit is either 0 or 5.
5. Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3.
6. Divisibility by 7: There is no easy rule for determining if a number is divisible by 7.
7. Divisibility by 8: A number is divisible by 8 if the last three digits of the number are divisible by 8.
8. Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
9. Divisibility by 10: A number is divisible by 10 if its last digit is 0.
10. Divisibility by 11: A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or divisible by 11.

Note that these are just general rules and may not always apply, especially for very large numbers.

Explanation with examples -

Divisibility by 2: A number is divisible by 2 if its units place has 0 or 2 or 4 or 6 or 8.

Example - 3450, 3502, 9324, 6536, 7618

All above numbers are divisible by 2 as these numbers have 0 or 2 or 4 or 6 or 8 in last digit.

Divisibility by 3: A number is divisible by 3 if the sum of digits is a multiple of 3.

Example - 852

 sum of digits = 8 + 5 + 2 = 15

 Since sum of digits (15) is divisible by 3, so number 852 is divisible by 3.

Divisibility by 4: 

Rule1 - A number is divisible by 4, if the number formed by its last 2 digits is divisible by 4. 

Examples - 40832 

Here last 2 digits form 32 which is divisible by 4,  so number 40832 is divisible by 4

Rule2 - Add twice the digit of the tens place to the digit of the unit place of the number.

Example - 5096 

(2 × 9) + 6 = 24

The number formed 24 which is divisible by 4, so number is divisible by 4.

Rule3 - If the digit at the tenth position is even and the unit place is 0, 4, or 8.

Example - 3548

Tenth place digit is 4 which is even and last digit is 8 so number 3548 is divisible by 4.

Rule4 - If the digit in the tens place is odd and the unit place is 2, or 6.

Example - 40832

Tenth place digit is 3 which is odd, and the last digit is 2 so number 40832 is divisible by 4.

Divisibility by 5: A number is divisible by 5 if its units place is 0 or 5. 

Example - 4565

Last digit is 5 so number is divisible by 5.

Divisibility by 6: A number is divisible by 6 if it is divisible by 2 and 3 both. 

Example - 96

Last digit is 6 (even number) so number is divisible by 2.

Sum of digits (9 + 6 = 15) which is divisible by 3 so number 96 is divisible by 3.