Prime Number Identification: Testing Numbers for Primality

Which of the numbers is a prime number?

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

• Step 1: Understand the definition of a prime number. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
• Step 2: Analyze and test each choice for primality:
• 45: Check divisibility by 2 (not even), by 3 (4 + 5 = 9, divisible by 3). Therefore, 45 is not prime.
• 46: Check divisibility by 2 (46 is even). Therefore, 46 is not prime.
• 42: Check divisibility by 2 (42 is even). Therefore, 42 is not prime.
• 43: Check divisibility by 2 (not even), by 3 (4 + 3 = 7, 7 is not divisible by 3), by 5 (does not end in 0 or 5). No divisors are found for 43. Hence, it is prime.

Upon checking, we see that 43 is the only number that cannot be evenly divided by any number other than 1 and itself. Thus, it is a prime number.

Therefore, the solution is $43$.