How can you determine if a number is prime?

How can you determine if a number is prime?

• A. It has exactly two distinct positive divisors: 1 and itself
• B. It is an even number greater than 2
• C. It can be divided by 5 without leaving a remainder
• D. It is a whole number greater than 10

Answer: (A)

A number is classified as a prime number if it has exactly two distinct positive divisors: 1 and itself. This means that a prime number can only be divided evenly (without leaving a remainder) by the number 1 and the number itself. For example, the number 7 is prime because it can only be divided by 1 and 7, resulting in whole numbers. In contrast, the other options do not accurately define prime numbers. An even number greater than 2, such as 4 or 6, has more than two positive divisors, disqualifying it from being prime. A number that can be divided by 5 is not necessarily prime since many numbers other than primes can be divided by 5, such as 10 or 15. Lastly, stating that a whole number greater than 10 is prime is misleading because there are many composite numbers greater than 10, such as 12, 14, and many others, which have divisors other than 1 and themselves. Therefore, the defining characteristic of a prime number being limited to exactly two positive divisors makes the first choice the accurate answer.

A number is classified as a prime number if it has exactly two distinct positive divisors: 1 and itself. This means that a prime number can only be divided evenly (without leaving a remainder) by the number 1 and the number itself. For example, the number 7 is prime because it can only be divided by 1 and 7, resulting in whole numbers.

In contrast, the other options do not accurately define prime numbers. An even number greater than 2, such as 4 or 6, has more than two positive divisors, disqualifying it from being prime. A number that can be divided by 5 is not necessarily prime since many numbers other than primes can be divided by 5, such as 10 or 15. Lastly, stating that a whole number greater than 10 is prime is misleading because there are many composite numbers greater than 10, such as 12, 14, and many others, which have divisors other than 1 and themselves. Therefore, the defining characteristic of a prime number being limited to exactly two positive divisors makes the first choice the accurate answer.