Thread: Expanded Euclidean Algorithm (calculating r and s)

1. Expanded Euclidean Algorithm (calculating r and s)

Hello!

Attached below inline is the work I've done in trying to figure out r and s from doing the Euclidean Algorithm in reverse. The original's file size was too large so I split it into top and bottom halves.

I've arrived at the correct GCD and plugged in all equations in reverse order. The math works out, meaning all the numbers combined do equal the GCD, but Im stuck as to what I have to combine to arrive at just two factors (r and s) that go together with the original numbers I started with.

Description of my photos:

The top half shows the two numbers I started with and the Euclidean Algorithm forwards to get the GCD of 60.
Right beneath that is the expansion of going in reverse up the list and filling in the equations.
Beneath THAT is the distribution of the factors and the final equation that that led to, which again works out.

The pairs on the right is me grouping the like terms. It looks like r is 90 which goes with 2,100 and s would be 8 which goes with 23,580, but Im left with an extra 180 and 480 that Im not sure what to do with. Thank you for your time!

2. Re: Expanded Euclidean Algorithm (calculating r and s)

I see what I was doing wrong. I had to simplify after every substitution. Thank you all anyway.

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