Can someone explain Euclid's Algorithm to me?

[1MileCrash]

My book is utterly useless - it vaguely gives me a history behind it, its motivations, and then lists an example in which it precedes to write a bunch of utterly false statements and then just.. spits out the answer.

Can someone explain to me what on Earth is going on in the attached picture? If this is not a notational confusion or typos in my book, then I must assert that Euclid's Algorithm makes absolutely no sense. 212 = 106.2, therefore here you go. I demand the author be sent to the lunatic asylum immediately.

 

[Integral]

How about you rotate that scan and try to get as much of the explanation as you can.

 

[1MileCrash]

Ok, I just looked it up online and it is fairly straight forward. I just don't understand how you can write the mathematical statement 212 = 106.2 + 0 and be ok with that. It makes me want to torch the book. I still have no idea what they are doing even after getting a coherent explanation.

 

[Mandelbroth]

My book is utterly useless - it vaguely gives me a history behind it, its motivations, and then lists an example in which it precedes to write a bunch of utterly false statements and then just.. spits out the answer.

Can someone explain to me what on Earth is going on in the attached picture? If this is not a notational confusion or typos in my book, then I must assert that Euclid's Algorithm makes absolutely no sense. 212 = 106.2, therefore here you go. I demand the author be sent to the lunatic asylum immediately.

1.106 is meaning 1 times 106, I think...

 

[1MileCrash]

1.106 is meaning 1 times 106, I think...

Oh thank goodness, now I don't have to switch majors.

Thanks you two.