A guest post by Dr. Cecily Zacharias from Oklahoma city, The United Sates of America. Currently she is an instructor at Oklahoma City Community College

**Rules for divisibility of 7 , 11 and 13**

It is equally good for 11 and 13.

Step 1 Divide into groups of three from the right. 245782 245 782

______________________________________________________________-1 1

Step 2. Write 1,-1,1,-1(alternate 1 and -1) in a row above the number 245 782

( start at the right end and go left)

____________________________________________________________-1 1

Step 3. Divide each Group by 7 (or 11 or 13, whatever the divisor is ) 245 782

0 5

** You can avoid step 2, by simply subtracting first remainder from the second. In this case it will be simply, 5 – 0 = 5*

Step 4. Multiply the corresponding numbers in the top row and bottom row and add 0x -1 + 5x 1 = 5

*** Step 4 can also be avoided. *

Step 5. a. If the sum obtained is zero, The number is divisible by 7 (or 11 or 13 )

b. If the sum is positive, then that is the remainder when we divide the number by 7 ( or 11 or 13 )

c. If the sum is negative, then add 7 (or 11 or 13 ) to get the remainder.

The sum is always less than the divisor.

In the example given, the sum is 5 . Which can be verified.

When 245782 is divided by 7 by long division, the quotient is 35111 and remainder is 5.

If we test for divisor 11, the bottom row will be 3 1

The sum of products of the two rows is -2. since it is negative , add 11 .

So the remainder will be 9

Actual division gives the quotient to be 22343 and remainder 9.

It is the same method for dividing by 13 too.

If you want you can simplify the steps 2 ,to 4 as

Find the remainders in each group and alternately add and subtract the remainders starting from the right. Then use step 5.

**On behalf of all the QuickerMaths.com users, I am highly grateful for her contribution. **

I was searching on internet for some stuff, i found here new unique thing which i didnt see before. New Rules for me

sorry but the method you have is not very clear can you give clear method of division .

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Sorry for my bad english. Thank you so much for your good post. Your post helped me in my college assignment, If you can provide me more details please email me.

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