DIVISIBILITY RULES

In factoring numbers, you should know if a certain number is divisible to another number. That's why there are divisibility rules that you have to know by heart (yes, you don't just memorize it). Don't worry, they are so simple that you can easily master them by yourself. Here they are:

1. A number is divisible by 2 if it ends with 0, 2, 4, 6, and 8. In short, the number should be an even number to be divisible by 2.

Example: 42, 74, 66, 98, and 230 are all divisible by 2.

2. A number is divisible by 3 if the sum of the digits of the number is divisible by 3.

Example: 753 is divisible by 3 (the sum of 7,5 and 3 is 15 which is divisible by 3)

3. A number is divisible by 4 if the two last digits of the number are both zeros or divisible by 4.

Example: 46,500 is divisible by 4 (last two digits are both zeros)

         875,144 is divisible by 4 (last two digits in this case is 44 which is divisible by 4)

4. A number is divisible by 5 if it ends with 5 or 0.

Example: 65 and 7,500 are both divisible by 5.

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

Example:  132 is divisible by 6 (it is divisible by 2 as well as divisible by 3)

6. A number is divisible by 7 if the number without the unit's digit minus twice the unit's digit is divisible by 7.

Example: 924 [ 92 - (4 * 2) = 84 ] 84 is divisible by 7 therefore, 924 is divisible by 7.

7. A number is divisible by 8 if the last three digits are all zeros or divisible by 8.

Example: 872,000 [last three digits are all zeros] - divisible by 8

274,168 [168 is divisible by 8] - divisible by 8

8. A number is divisible by 9 if the sum of its digits is divisible by 9.

Example: 2,718 [2+7+1+8 = 18] 18 is divisible by 9 so, 2,718 is divisible by 9

9. A number is divisible by 10 if it ends with 0.

Example: 784,280 - divisible by 10.

10. A number is divisible by 12 if it is divisible by both 3 and 4.

Example: 7,500 [divisible by 3 and 4] - divisible by 12

11. Real number (10^n) - 1 [n is a natural number] is divisible by 9. If n is even, (10^n) - 1  is divisible by 11.

Example:  (10^5) - 1 = 100,000 - 1 = 99,999 is divisible by 9 [n=5, odd]

 (10^4) - 1 = 10,000 - 1 = 9,999 is divisible by 9 and 11 [n=4, even]


I'll be having worksheets for this. So, watch out for that. In the meantime, absorb everything you can from these basic rules.