Learning MATHS

TODAY I AM GOING TO PUBLISH
General Divisibility Rule
By A Two Digit Number
I noticed there is no single rule for divisibility of a number by another number. Of course there are rules for distinct numbers which are different from each other. I felt the requirement of a general rule.
The utility of the rule will be determined by Students & Teacher.
A number of (n+1) digits is given by :- N=a0+10a1+100a2+1000a3+.................+10nan is divisible by a two digit number 10r+p [ where ,1 r,p 9 ] if
[ a1+10a2+100a3+...........+10n-1an] + qa0 =(10r+p)w [w is a whole number],where “q” is a number to be found out.
Proof:- Now given number N=a0+10a1+100a2+1000a3+..........+10nan
=a0+10(a1+10a2+100a3+1000a4+...........+10n-1an)
=a0 +10{ (10r+p)w - qa0}
=a0(1-10q) +10w(10r+p)
Hence given number “N” divisible by 10r+p if 1-10q =(10r+p)w0 [ w0 is a whole number]
Let's check divisibility of 2941 by17.Here a0 =1,10r+p=17. Hence
1(1-10q) =17w0 ,i.e minimum value of “q”is -5,to make the left side a multiple of 17. Now 2941 leaving the unit place becomes 294. 294-51 =289 which is divisible by17. So 2941divisible by 17 too.