Prime numbers are foundational in number theory and crucial for many mathematical applications. A prime number is an integer greater than 1 that has no positive divisors other than 1 and itself. This means that if you try to divide a prime number by any other number except 1 and itself, you will get a remainder. For instance, 7 is a prime number because the only divisors of 7 are 1 and 7. Conversely, 6 is not a prime number because it can be divided evenly by 1, 2, 3, and 6.
To identify a prime number, follow these steps:
- Check divisibility by numbers starting from 2 up to the square root of the number in question.
- If none of these numbers divide the number entirely (i.e., without leaving a remainder), then the number is prime.
Understanding primes is central to this exercise as it helps narrow down possibilities in a given number range.