Quiz 2, MAT115R

Make sure that your name is on your paper. There are 10 points total. Show work!

1. (3 pts) Define the following:
   1. Counting numbers: positive integers; positive whole numbers; natural numbers 1,2,3,4,etc.;
   2. Prime number: counting numbers with exactly two distinct factors, 1 and themselves.
   3. Composite number: counting numbers with three or more distinct factors.
   

   

2. (1 pt) State the prime factorization theorem.

   Theorem (prime decomposition or prime factorization): every natural number (other than 1) is either prime, or can be written as a product of primes in a unique way, from smallest to largest.

   In the examples above, one person missed the restriction to counting numbers greater than 1, and uniqueness; the other used the word "unique", which pleased me!

3. (4 pts) Decide if either of these numbers is prime (show work!). If a number is not prime, draw a tree to show its prime factors.
   1. 167
   2. 221
   

4. (2 pts) Draw the complete graph that corresponds to the the number 6, \(K_6\).