8. Prime Numbers and GCD

Try these first

1. 1.

   What is the smallest prime number?

   Hint

   Think about the smallest integer greater than one.

2. 2.

   How many prime numbers are there between 1 and 10?

   Hint

   Count the prime numbers in that range.

3. 3.

   What is the GCD of 24 and 36?

   • 6
   • 12
   • 18

   Hint

   Calculate the common divisors of the two numbers.

4. 4.

   True or False? The number 9 is a prime number.

   • True
   • False

   Hint

   Recall the definition of prime numbers.

5. 5.

   Using the application of Euclid's algorithm, find the GCD of 215 and 995. Explain each step.

   Hint

   Remember to keep finding the remainder until you reach 0.

6. 6.

   Construct a proof to outline why infinite primes exist, possibly using a method similar to Euclid’s.

   Hint

   Focus on contradiction and prime factorization concepts.