Divisibility rules

[dwei1019]

Does anyone kow the divisibility rules from 1 to 17?
Thanks!

[PowerOfPi]

You can find the 1-12 rules here. I haven't 13-17 a lot, so I just resort to plain dividing when they come up.

[fishythefish]

1) is automatically true.

2) is all even numbers (the last digit is 0, 2, 4, 6, or 8)

3) is if the sum of the digits is a multiple of three. (Note: if the sum is greater than 9, just sum again! Then you only have to know , , , and .)

4) is if the last two digits are divisible by 4, if you can divide by 2 twice, if the 10s digit plus twice the 1s digit is divisible by 4, if the 10s digit is even, and the 1s digit is 0, 4, 8, or if the 10s digit is odd, and the 1s digit is 2, 6.

5) The last digit is 0 or 5.

6) It's divisible by both 2 and 3, or if the last digit multiplied by the sum of the other digits is divisible by 6.

7) From right to left, create blocks of 3 digits. Form an alternating sum of the blocks, from right to left. (For example, 6049344 would be (+)344 - 049 + 6 = 301.) Subtract 2 twice the last digit from the rest of the number or add 5 times the last digit to the rest of the number and check to see if the result is divisible by 7.

8) The last 3 digits are divisible OR add the last digit to twice the sum of the others and check if it's divisible by 8 OR if the 100s digit is even, check the last two digits, or if the 100s digit is odd, check the last two digits plus 4.

9) The sum of the digits (repeat as necessary, like number 3) is 9.

10) The last digit is 0.

11) Subtract the last digit from the rest of the number and check OR add the digits in 2-digit block from right to left and check OR form an alternating sum of digits and check. (Example: 136004 1-3+6-0+0-4 = 0, which is divisible by 11.)

12) If it is divisible by 3 and 4 OR subtract the last digit from two times the rest of the number and check.

13) Add 4 times the last digit to the rest of the number and check OR add the digits in alternate 3-digit blocks from right to left, then take the difference of the sums and check. (Example: 1604928 (928 + 1) - (604) = 325, which, if you check, is 13 times 25.)

14) Divisible by 2 and 7 OR the last two digits plus two times the rest of the number is divisible by 14.

15) Divisible by 5 and 3

16) If the 1000s digit is even, check the last three digits. If the 1000s digit is odd, check the last three digits plus 8. OR truncate the last two digits, multiply by 4, then add the last two digits and check.

17) Subtract 5 times the last digit from the rest of the number.

18) Divisible by 2 and 9.

19) Add two times the last digit to the rest of the number.

20) Divisible by 2 and 10 OR the last digit is 0 and the 10s digit is even, or the number formed by the last two digits is divisible by 20.

Also see http://en.wikipedia.org/wiki/Divisibility_rule

I tried to give examples for the more confusing, but if you need more, let me know.

[salahcool]

IN THE NAME OF GOD


Dividing by 2


All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8.

Dividing by 3

Add up all the digits in the number.
Find out what the sum is. If the sum is divisible by 3, so is the number
For example: 12123 (1+2+1+2+3=9) 9 is divisible by 3, therefore 12123 is too!


Dividing by 4

Are the last two digits in your number divisible by 4?
If so, the number is too!
For example: 358912 ends in 12 which is divisible by 4, thus so is 358912.
Dividing by 5

Numbers ending in a 5 or a 0 are always divisible by 5.
Dividing by 6

If the Number is divisible by 2 and 3 it is divisible by 6 also.
Dividing by 7 (2 Tests)

Take the last digit in a number.
Double and subtract the last digit in your number from the rest of the digits.
Repeat the process for larger numbers.
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.

Dividing by 8

This one's not as easy, if the last 3 digits are divisible by 8, so is the entire number.
Example: 6008 - The last 3 digits are divisible by 8, therefore, so is 6008.
Dividing by 9

Almost the same rule and dividing by 3. Add up all the digits in the number.
Find out what the sum is. If the sum is divisible by 9, so is the number.
For example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!
Dividing by 10

If the number ends in a 0, it is divisible by 10.

thanks
salahcool

[cgyao15]

you should write WHY not just the rules.
e.g it's 4 because everything in the hundreds is divisible by 4 so the last 2 digits, need to be divisible by 4.
like 724 is divisible by 4 because 700/4 and 24/4 leave no remainder.

[AIME15]

salahcool: Nice, stolen from here

fishythefish: You have a small typo in 20); it should be "divisible by 4 and 10".

[fishythefish]

Yeah, I just discovered that, too. What I meant is that it is divisible by 10, then by 2, or vice versa; hence, the other rules.

A lot of the rules can be interpreted more than one way, but I tried to make them clear.

[johnswhite]

Those are the goods divisibility rules. I recommend QUICKER MATHS BY M. TYRA book. It is the best book for doing the maths quickly. I like the book so much. You can calculate so fastly. It is including all the parts of maths.