Can someone explain Euclid's Algorithm to me?

In summary, the conversation discusses frustrations with a book on Euclid's Algorithm and confusion over a mathematical statement. The speaker expresses disappointment in the book and demands the author be sent to a lunatic asylum. After receiving clarification, the speaker is relieved and grateful.
  • #1
1MileCrash
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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.
 

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  • #2
How about you rotate that scan and try to get as much of the explanation as you can.
 
  • #3
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.
 
  • #4
1MileCrash said:
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...
 
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Likes Michael Hardy
  • #5
Mandelbroth said:
1.106 is meaning 1 times 106, I think...

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

Thanks you two.
 

1. What is Euclid's Algorithm?

Euclid's Algorithm is a method for finding the greatest common divisor (GCD) of two numbers. It is named after the ancient Greek mathematician Euclid, who described the algorithm in his book "Elements".

2. How does Euclid's Algorithm work?

The algorithm works by repeatedly dividing the larger number by the smaller number and using the remainder as the new smaller number. This process is repeated until the remainder is equal to 0. The last non-zero remainder is the GCD of the two numbers.

3. Why is Euclid's Algorithm important?

Euclid's Algorithm is important because it is a fast and efficient method for finding the GCD of two numbers. It is also the basis for many other important mathematical concepts, such as modular arithmetic and the extended Euclidean algorithm.

4. Can you provide an example of Euclid's Algorithm being used?

Sure, let's find the GCD of 24 and 36 using Euclid's Algorithm. Step 1: 36 ÷ 24 = 1 with a remainder of 12 Step 2: 24 ÷ 12 = 2 with a remainder of 0 Step 3: Since the remainder is 0, the GCD is the last non-zero remainder, which is 12. Therefore, the GCD of 24 and 36 is 12.

5. Is Euclid's Algorithm only used for finding the GCD?

No, Euclid's Algorithm can also be used for other purposes such as simplifying fractions, finding multiplicative inverses, and solving certain types of equations. It is a versatile and powerful tool in mathematics.

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