Number Theory Practice: Identifying Prime Numbers from a Set

Which of the numbers is a prime number?

To determine which of the given numbers is a prime number, follow these steps:

• Step 1: Check the number 39.
  39 is divisible by 3 (since 3 + 9 = 12, which is divisible by 3), so it has divisors other than 1 and itself, and thus 39 is not prime.
• Step 2: Check the number 34.
  34 is divisible by 2 (as it's an even number), so it has divisors other than 1 and itself, and thus 34 is not prime.
• Step 3: Check the number 42.
  42 is divisible by 2 (as it's an even number), so it has divisors other than 1 and itself, and thus 42 is not prime.
• Step 4: Check the number 37.
  For a number to be prime, it should not be divisible by any numbers other than 1 and itself. We check divisibility of 37 by numbers up to its square root (~6.08), which are 2, 3, and 5.
• 37 is not divisible by 2 (as it is odd).
• 37 is not divisible by 3 (as 3 + 7 = 10, which is not divisible by 3).
• 37 is not divisible by 5 (as it does not end in 0 or 5).

Since 37 is not divisible by any integer other than 1 and 37 itself, it is a prime number.

Therefore, the solution to the problem is $37$.