CHAPTER 5
Number Theory
5.1. Primes, Composites, and Tests for Divisibility
Definition. A counting number with exactly two di↵erent factors is called
a prime number or a prime. A counting number with more than two factors is
called a composite number, or a composite.
The Sieve of Eratosthenes is a tool used to find primes.
Start by circling 2 and then crossing out every second number. Then circle
3 and cross out every third number. Do the same for 5, 7, etc. The circled
numbers are primes and the crossed out numbers are composites.
Note. The number 1 is neither prime nor composite.
Factor trees can be used to express a composite as a product of smaller numbers
and even as a product of primes.
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