An Empirical way to find divisibility

Here is an empirical way to find if a number N1 is divisible by another number N2

This can be applied to larger numbers as well. I am giving an illustrative example below with smaller numbers which can be easier to comprehend here

Say for example you want to find out if 192 is divisible by 24

Divisor is 192 and Dividend = 24

Here is the technique

Calculate for the

Divisor                  x1 = 192 mod 10 = 2                         y1 = 192 div 10 = 19

One time Calculation for the

Dividend              x2 = 24 mod 10 = 4                                           y2 = 24 div 10 = 2

Find – New Divisor = abs(x2*y1 – x1*y2) = 19*4 – 2*2 = 72

Now repeat the above steps with the new Divisor

Calculate for the

Divisor                  x1 = 72 mod 10 = 2                           y1 = 72 div 10 = 7

Find – New Divisor = abs(x2*y1 – x1*y2)  = 7*4 – 2*2 = 24

Since the new Divisor is Equal to the Dividend we infer that the Original Number 192 is divisible by 24

 

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s