Another general method-divisibility tests

I am now introducing details another general method for divisibility tests.
Let me show the way for conducting a test for divisibility by 19.
Number to be tested-4783915
Break this into 2 parts-478391 and 5
Multiply the second part by 2 and add to first part-478391+10=478401
Repeat the procedure-47840+2=47842
Repeat again-4784+4=4788
Repeat 478+16=494-
Test the result for divisibility.--494 is divisible by 19 and so is therefore the original start number 4783915
Another Example-Number to be tested-15857799
1585779+18=1585797....158579+14=158593...15859+6=15865..1586+10=1596
159+12=171...171 is divisible by 19 and so is original start number 15857799
Similar  method can be adopted for conducting test for divisibility by other numbers like 17,23,29 ,79,89 etc
However the number to be used for multiplying the second part in each case is different-they are shown below-
For 17 it is 12
For 23 it is 7
For 29 it is 3
For 79 it is 8
For 89 it is 9
You will notice that these are the same numbers which can be worked out based on my blog Multipliers-Rejoinder posted a couple of days back.-though with reference to cyclic numbers.
Try numbers 159327944.....,65482725,....45327029331.-for testing divisibility by 17