Greatest Common Divisors Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Find the greatest common divisor of each of the following pairs of integers:

    (a)    (b) 0,100   (c)    (d)    (e) 100, 121   (f) 1001, 289

(2) Let b a positive integer. What is the greatest common divisor of and

(3) Let b a positive integer. What is the greatest common divisor of and

(4) Let b a positive integer. What is the greatest common divisor of and

(5) Let b a positive integer. What is the greatest common divisor of and

(6) Show that if and are integers with then or 2.

(7) Show that if and are even integers that are not both zero, then

(8) Sow that if and are integers such that and then

(9) Show that if and are integers with then

(10) Show that if is a positive integer, then and are relatively prime.

(11) Show that and are relatively prime for all integers

(12) Show that if and are relatively prime integers, then or 3.

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