How do you identify a prime number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

To identify a prime number, you need to check if it can be divided evenly by any number other than 1 and itself. Start by dividing the number by 2. If it divides evenly (i.e., without leaving a remainder), it is not a prime number. If it does not, proceed to the next odd number, which is 3, and continue this process with subsequent odd numbers (5, 7, 11, etc.) up to the square root of the number you are testing.

For example, let's determine if 29 is a prime number. First, check if 29 is divisible by 2. Since 29 is odd, it is not divisible by 2. Next, check if it is divisible by 3. The sum of the digits of 29 is 11 (2 + 9), and since 11 is not divisible by 3, 29 is not divisible by 3. Continue with 5; since 29 does not end in 0 or 5, it is not divisible by 5. The next number to check is 7, and since 29 divided by 7 does not result in a whole number, 29 is not divisible by 7. Since we have checked all numbers up to the square root of 29 (which is approximately 5.39), and none of them divide 29 evenly, we can conclude that 29 is a prime number.

Remember, the key steps are to test divisibility by all prime numbers up to the square root of the number in question. This method ensures you efficiently determine whether a number is prime.