e)+Divisibility+Rules

What are the divisibility rules for 1-12? Be sure to include where you found the information.

posted by : **smokey-dice1212**

**Dividing by 3**
 * Dividing by 2 **
 * 1) All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8.
 * 1) Add up all the digits in the number.
 * 2) Find out what the sum is. If the sum is divisible by 3, so is the number
 * 3) For example: 12123 (1+2+1+2+3=9) 9 is divisible by 3, therefore 12123 is too!

>  > **NEXT TEST** -
 * Dividing by 4 **
 * 1) Are the last two digits in your number divisible by 4?
 * 2) If so, the number is too!
 * 3) For example: 358912 ends in 12 which is divisible by 4, thus so is 358912.
 * Dividing by 5 **
 * 1) Numbers ending in a 5 or a 0 are always divisible by 5.
 * Dividing by 6 **
 * 1) If the Number is divisible by 2 and 3 it is divisible by 6 also.
 * Dividing by 7 (2 Tests) **
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Take the last digit in a number.
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Double and subtract the last digit in your number from the rest of the digits.
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Repeat the process for larger numbers.
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Example: 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7.
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Take the number and multiply each digit beginning on the right hand side (ones) by 1, 3, 2, 6, 4, 5. Repeat this sequence as necessary
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Add the products.
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">If the sum is divisible by 7 - so is your number.
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Example: Is 2016 divisible by 7?
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">6(1) + 1(3) + 0(2) + 2(6) = 21
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">21 is divisible by 7 and we can now say that 2016 is also divisible by 7.
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Dividing by 8 **
 * 1) <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">This one's not as easy, if the last 3 digits are divisible by 8, so is the entire number.
 * 2) <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Example: 6008 - The last 3 digits are divisible by 8, therefore, so is 6008.
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Dividing by 9 **
 * 1) <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Almost the same rule and dividing by 3. Add up all the digits in the number.
 * 2) <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Find out what the sum is. If the sum is divisible by 9, so is the number.
 * 3) <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">For example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Dividing by 10 **
 * 1) <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">If the number ends in a 0, it is divisible by 10.

Posted by: **DummyDerrick** divisible by: ||~ If: ||~ Example: || 12**9** is not || 217 (2+1+7=10, and 10÷3 = 3 1/3 ) **No** || 70**19** is not || 80**9** is not ||
 * ~ A number is
 * 2 || The last digit is even (0,2,4,6,8) || 12**8** is
 * 3 || The sum of the digits is divisible by 3 || 381 (3+8+1=12, and 12÷3 = 4) **Yes**
 * 4 || The last 2 digits are divisible by 4 || 13**12** is (12÷4=3)
 * 5 || The last digit is 0 or 5 || 17**5** is
 * 6 || The number is divisible by both 2 //and// 3 || 114 (it is even, and 1+1+4=6 and 6÷3 = 2) **Yes**

308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3 ) **No** || (Note: you can apply this rule to that answer again if you want) || 672 (Double 2 is 4, 67-4=63, and 63÷7=9) **Yes** 905 (Double 5 is 10, 90-10=80, and 80÷7=11 3/7 ) **No** || 216**302** (302÷8=37 3/4 ) **No** ||
 * 7 || If you double the last digit and subtract it from the rest of the number and the answer is: * **0**, or
 * **divisible by 7**
 * 8 || The last three digits are divisible by 8 || 109**816** (816÷8=102) **Yes**
 * 9 || The sum of the digits is divisible by 9

(Note: you can apply this rule to that answer again if you want) || 1629 (1+6+2+9=18, and again, 1+8=9) **Yes** 2013 (2+0+1+3=6) **No** || 22**1** is not || 3**7**2**9** ((7+9) - (3+2) = **11**) **Yes** 2**5**1**7**6 ((5+7) - (2+1+6) = **3**) **No** || 916 (9+1+6=16, 16÷3= 5 1/3 ) **No** ||
 * 10 || The number ends in 0 || 22**0** is
 * 11 || If you sum every second digit and then subtract all other digits and the answer is:
 * **0**, or
 * **divisible by 11** || 1**3**6**4** ((3+4) - (1+6) = **0**) **Yes**
 * 12 || The number is divisible by both 3 //and// 4 || 648 (6+4+8=18 and 18÷3=6, also 48÷4=12) **Yes**

http://www.mathsisfun.com/divisibility-rules.html
 * http://math.about.com/library/bldivide.htm