Understanding Number Systems - 2 - Divisibility of Numbers.

This is the 2nd post on Number Systems. For 1st post, click here.

Todays post will deal with Divisibility rules of Numbers. This is very useful when finding if a number is Prime or not, factoring a number etc.

Rules:

1. A number is said to be divisible by 2 if its unit digit is 0 or even. Eg (14, 998, 2000 etc)
2. A number is said to be divisible by 3 if the sum of its digits is divisible by 3. (Eg : 1431, 6, 27 etc).
3. A number is said to be divisible by 4 if its last two digits are 0 each or the number formed by them is completely divisible by 4. (Eg: 100, 9999904 etc)
4. A number is said to be divisible by 5 if its last digit is 0 or 5.
5. A number is said to be divisible by 6 if its unit digit is 0 or even and sum of its digits is divisible by 3. (6, 18, 96 etc).
6. A number is said to be divisible by 8 if its last three digits are 0 each or the number formed by them is completely divisible by 8 (Eg: 16, 128, 1111128 etc).
7. A number is said to be divisible by 9 if the sum of its digits is divisible by 9. (Eg 9, 9801, 774 etc).
8. A number is said to be divisible by 10 if its unit digit is 0. (Eg 10, 100 etc)
9. A number is said to be divisible by 11 if the difference of the sum of its digits in the odd place and the sum of its digits in the even place is either 0 or a multiple of 11 ( Eg. 121, 1331 etc)

Divisibility by 11 using examples:

Consider the number 187968.

Since the difference 11 is divisible by 11,  187968 is divisible by 11!