Find the GCD(137, 215) using the Euclidean Algorithm. Are they relatively prime? Show your work!!!

In your own words, explain the division algorithm. Pick two examples that you would use in class to explain this algorithm. Why did you pick those examples?

Find the LCM of the following using Euclidean Algorithm. 1. [48,32] 2. [35,50] 3. [75, 325] 4. [252,182] 5. [36, 64, 112] 6. [9a + 8,6a + 5]

This question is about Perfect Codes in Coding Theory: You may use that a perfect code of length 13 and distance 3 exists over GF(3). A soccer betting form contains a list of 13 matches. Next to each listed match there are three fill-in boxes which correspond to the following three possible guesses: “first team wins”, “second team wins” or “tied match”. The bettor checks one box for each match. Describe a strategy for filling out the smallest number of forms so that at least one of the forms contains at least 12 correct guesses. How many forms need to be filled out under this strategy?