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Methods Of Determining Dividability For Prime Numbers --------------------------------------------------------
As we all know ,there are some
methods for testing dividability on some numbers such as 2, 3, 5, 9, 11.
Eg: - To be dividable into two ,
the last right digit should be an even digit. - To be dividable into 5, the
last right digit should be either 5 or 0. - To be dividable into 3, the
sum of all the digits should be dividable into three. - To be dividable into 9, the
sum of all the digits should be dividable into nine. - To be dividable into 11, the
sum of all the digits should be dividable into 11after assigning
consecutive plus and minus to thedigits from the rigth. for
example, the number 7271 conld be assigned as 7271 and the sum would be
-11 which signifies dividability. Now, some of new methods for
determining dividability are presented, which have developed by me. At first, I described a
dividability code for each prime number. ------------------------------------- Dividability into seven ( 7 ) ------------------------------------------- The dividability code into 7 is 2 (two). The following example illustrate this. In each step, the code is multiplied by the last digit on the right and subtracted from the remaining digits. 179739----------------------------------------------------------17973 - 9 * 2 17955-----------------------------------------------------------1795 - 5 * 2 1785------------------------------------------------------------ 178 - 5 * 2 168 ------------------------------------------------------------- 16 - 8 * 2 0 The remainder is either zero or a multiple of seven. It is noteworthy that at each step the result is a multiple of seven itself. If the considered number is not a multiple of seven, the remainder of the division shouldbe determined.To do this, I have described the following pattern. E.g:What is the remainder of the division of the number 89367471 into seven ? 2------------------------------ 89367471---------------------------8936744 -1 * 2 3 ------------------------------8936742----------------------------893674 - 2 * 2 1------------------------------ 893670-----------------------------893676 - 0 * 2 5------------------------------ 89367 ------------------------------8936 - 7 * 2 6------------------------------ 888---------------------------------88 - 8 * 2 2------------------------------ 72----------------------------------7 - 2 * 2 3------------------------------ 3 The last remainder is determined and the previous remainders according to the above-mentioned pattern, in an anti-clockwise order. Thus the final remainder is determined.----------------------------------------- Dividability into forty three (43) ----------------------------------------------------- The dividability code is thirty (30) 775935 --------------------------------------------------------------77593 - 5 * 30 77443 ---------------------------------------------------------------7744 - 3 * 30 7654 ----------------------------------------------------------------765 - 4 * 30 645 ------------------------------------------------------------------64 - 5 * 30 86 86 = 2 * 43 As it is obvious, the result is a multiple of 43. This is the same as the method for determining dividability into seven. |
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