Friday 10 February 2012

Divisibility test for 41-also general formula for such tests

I am now presenting a test for divisibility of numbers by the prime number 41.This is based on a general formula useful for testing divisibility by any other prime number say 17,19,23,29,31,43 ...etc
In the case of each prime,you will have to remember certain numbers for testing the divisibility.
For 41, you will have to remember the numbers...1,10,18,16 and 37
Example of number to be tested-1174814....
Step 1-Read the digits from right to left...4,1,8,4,7,1,1
Step2-Multiply these digits successively by the numbers mentioned above viz 1,10,18,16,37,1,10
Step3-Add up the products-(4*1)+(1*10)+(8*18)+(4*16)+(7*37)+(1*1)+(1*10)=4+10+144+64+259+1+10=492.
Step 4-Test the result for  divisibility by 41..If the result is divisible by 41,the number under test will be divisible by 41.In our example 492 is divisible by 41 and so 1174814 will be divisible.
Try testing more numbers say 4560102...1330573..
I will explain in a future blog how the numbers 1,10,18,16 and 37 were arrived at.If you know the method,there will be no necessity to remember them.
Depending on the number of digits in the number under test,you can use the numbers 1,10,18,16,37 given by me successively-like me using 1,and 10 for the 6th and 7th  digits. 

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