8.1. Introduction to Prime Numbers

Try these first

1. 1.

   Define a prime number.

   Hint

   Think about the divisors.

2. 2.

   List three prime numbers.

   Hint

   Remember the smallest integers.

3. 3.

   What defines a prime number?

   • An integer greater than 1 with only 1 and itself as divisors
   • An even number
   • An integer less than 1

   Hint

   It has to be greater than 1.

4. 4.

   True or False: All prime numbers are odd.

   • True
   • False

   Hint

   Remember exceptions to the rule.

5. 5.

   Using the naive algorithm, prove that 37 is a prime number.

   Hint

   Look closely at the range of possible divisors closely.

6. 6.

   Find the GCD of 210 and 45 using Euclid's algorithm and explain each step.

   Hint

   Follow the modulus steps step by step carefully.