8.2. Properties of Prime Numbers

Try these first

1. 1.

   Define a prime number.

   Hint

   Remember that 2 is the only even prime number.

2. 2.

   Give an example of a composite number.

   Hint

   Think of some even numbers.

3. 3.

   What defines a prime number?

   • Divisible by only 1
   • Divisible by 1 and itself
   • Divisible by multiple factors

   Hint

   Recap what makes primes unique.

4. 4.

   True or False: Every even number greater than 2 is prime.

   • True
   • False

   Hint

   Consider the definition of prime numbers.

5. 5.

   Calculate the GCD of 252 and 105 using Euclid's algorithm step-by-step.

   Hint

   Use the modulo operation to continually replace the numbers.

6. 6.

   Prove that there are infinitely many prime numbers using contradiction.

   Hint

   Think about divisibility and what adding one does.