Question 1: List all prime numbers between 1 and 20.

Answer: 2, 3, 5, 7, 11, 13, 17, 19

Question 2: Identify which of the following numbers are prime: 21, 23, 25, 29.

Answer: 23, 29

Question 3: Is 31 a prime or a composite number? Explain your reasoning.

Answer: Prime, because it has only two factors: 1 and 31.

Question 4: Construct a number that is composite but has exactly three factors. Describe it.

Answer: For example, 9 (factors: 1, 3, 9).

Question 1: A number is divisible by 2, 3, and 5. Could it be prime? Why or why not?

Answer: No, because a prime number has only two factors. A number divisible by 2, 3, and 5 has at least these factors, so it cannot be prime.

Question 2: Find a composite number less than 50 that is divisible by exactly three distinct primes. Show your work.

Answer: 30 (factors: 2, 3, 5)

Question 1: A school is assigning lockers. The lockers are numbered from 1 to 100. Which locker numbers are prime? Why might prime numbers be special in this context?

Answer: Prime numbers are special because they can only be divided by 1 and themselves, which might be useful for assigning unique or special lockers.

Question 1: Prove that 29 is a prime number using divisibility tests.

Answer: 29 is not divisible by 2, 3, 5, 7, 11, 13, 17, 19, or 23. Since it has no divisors other than 1 and itself, it is prime.

Question 2: Find the smallest composite number that is a multiple of both 3 and 4 but not prime.

Answer: 12

Question 1: Statement: All prime numbers are odd. Is this true? Fix the statement if necessary.

Answer: False, because 2 is a prime number and it's even. Corrected: Not all prime numbers are odd; 2 is an even prime.

Question 2: A student says: 'Every number greater than 1 is either prime or composite.' Is this correct? Explain.

Answer: Yes, this is correct because every number greater than 1 is either prime (has exactly two factors) or composite (has more than two factors).