Final answer:
1 is not considered a prime number because it only has one positive divisor, itself, not the required two. Negative numbers cannot be prime as they must be positive. Attention must be paid to the signs of numbers in operations.
Step-by-step explanation:
Prime numbers are defined as natural numbers greater than 1 that are not products of two smaller natural numbers. The number 1 is not considered a prime number because it has only one positive divisor, itself, which does not meet the required definition of having two distinct positive divisors. In the case of negative numbers, by definition, prime numbers must be positive; negative numbers do not qualify because they do not satisfy the basic property of having two positive divisors (one and the number itself).
When working with whole numbers, attention must be paid to the signs of the numbers, especially in operations like multiplication. Two positive numbers will result in a positive number, just as multiplying two negative numbers will, due to the multiplication rules for signs. Differently signed numbers, when multiplied, result in a negative number. These rules help ensure the correct application of operations with whole numbers.