Question 1: Calculate whether 37 is a prime number. Show your working.

Answer: Yes, 37 is prime because it has no divisors other than 1 and 37.

Question 2: Determine if 49 is prime. Explain your reasoning.

Answer: No, 49 is not prime because it is divisible by 7.

Question 3: List all prime numbers between 10 and 20.

Answer: 11, 13, 17, 19

Question 4: Use divisibility rules to determine if 121 is prime. Show your working.

Answer: No, 121 is divisible by 11 because 11×11=121, so it is not prime.

Question 5: Identify whether 97 is prime and justify your answer.

Answer: Yes, 97 is prime because it has no divisors other than 1 and itself.

Question 6: A number is divisible by 3 if the sum of its digits is divisible by 3. Use this rule to determine if 123 is prime.

Answer: 123 is divisible by 3 because 1+2+3=6, which is divisible by 3, so 123 is not prime.

Question 7: Construct a list of five prime numbers greater than 50.

Answer: 53, 59, 61, 67, 71

Question 8: Explain why 91 is not a prime number, including its factors.

Answer: 91 is not prime because it has factors 7 and 13 (7×13=91).

Question 9: Identify all prime numbers less than 30 and greater than 20.

Answer: 23, 29

Question 10: Determine whether 100 is prime. Show your reasoning.

Answer: No, 100 is not prime because it is divisible by 2, 5, and other numbers.

Question 11: Identify any errors in the statement: 'All prime numbers are odd.'

Answer: The statement is incorrect because 2 is prime and even, so not all prime numbers are odd.