• Table of Contents

  • Which One of the Following is Not a Prime Number?
  • Understanding Prime Numbers
  • Identifying Prime Numbers
  • Which One of the Following is Not a Prime Number?
  • Summary
  • Q&A

Prime numbers are a fascinating concept in mathematics. They are the building blocks of the number system and have unique properties that make them distinct from other numbers. In this article, we will explore the concept of prime numbers and answer the question, “Which one of the following is not a prime number?”

Understanding Prime Numbers

Before we delve into the question at hand, let’s first understand what prime numbers are. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In simpler terms, it is a number that cannot be divided evenly by any other number except 1 and itself.

For example, the first few prime numbers are 2, 3, 5, 7, 11, and so on. These numbers are only divisible by 1 and themselves, making them unique in the number system.

Identifying Prime Numbers

Now that we know what prime numbers are, let’s discuss how to identify them. There are several methods to determine whether a number is prime or not. One of the most common methods is the trial division method.

In the trial division method, we divide the number in question by all the numbers less than it and check if any of them divide it evenly. If we find a divisor other than 1 and the number itself, then the number is not prime. Otherwise, it is prime.

For example, let’s consider the number 17. We divide it by all the numbers less than it:

• 17 ÷ 2 = 8.5 (not divisible)
• 17 ÷ 3 = 5.67 (not divisible)
• 17 ÷ 4 = 4.25 (not divisible)
• 17 ÷ 5 = 3.4 (not divisible)
• 17 ÷ 6 = 2.83 (not divisible)
• 17 ÷ 7 = 2.43 (not divisible)
• 17 ÷ 8 = 2.125 (not divisible)
• 17 ÷ 9 = 1.89 (not divisible)
• 17 ÷ 10 = 1.7 (not divisible)
• 17 ÷ 11 = 1.54 (not divisible)
• 17 ÷ 12 = 1.42 (not divisible)
• 17 ÷ 13 = 1.31 (not divisible)
• 17 ÷ 14 = 1.21 (not divisible)
• 17 ÷ 15 = 1.13 (not divisible)
• 17 ÷ 16 = 1.06 (not divisible)

As we can see, none of the numbers less than 17 divide it evenly. Therefore, 17 is a prime number.

Which One of the Following is Not a Prime Number?

Now, let’s address the question at hand: “Which one of the following is not a prime number?” To answer this question, we need to consider the following options:

1. 15
2. 23
3. 29
4. 37

To determine which one of these numbers is not a prime number, we can apply the trial division method as discussed earlier.

Let’s start with the first option, 15:

• 15 ÷ 2 = 7.5 (not divisible)
• 15 ÷ 3 = 5 (divisible)

Since 15 is divisible by 3, it is not a prime number. Therefore, the answer to the question is option 1: 15 is not a prime number.

Now, let’s briefly check the remaining options:

• 23 ÷ 2 = 11.5 (not divisible)
• 23 ÷ 3 = 7.67 (not divisible)
• 23 ÷ 4 = 5.75 (not divisible)
• 23 ÷ 5 = 4.6 (not divisible)
• 23 ÷ 6 = 3.83 (not divisible)
• 23 ÷ 7 = 3.29 (not divisible)
• 23 ÷ 8 = 2.875 (not divisible)
• 23 ÷ 9 = 2.56 (not divisible)
• 23 ÷ 10 = 2.3 (not divisible)
• 23 ÷ 11 = 2.09 (not divisible)
• 23 ÷ 12 = 1.92 (not divisible)
• 23 ÷ 13 = 1.77 (not divisible)
• 23 ÷ 14 = 1.64 (not divisible)
• 23 ÷ 15 = 1.53 (not divisible)
• 23 ÷ 16 = 1.44 (not divisible)

Since none of the numbers less than 23 divide it evenly, 23 is a prime number. The same applies to options 3 (29) and 4 (37). Therefore, the answer to the question is option 1: 15 is not a prime number.

Summary

Prime numbers are unique numbers in the number system that have no positive divisors other than 1 and themselves. They play a crucial role in various mathematical concepts and applications. In this article, we explored the concept of prime numbers and answered the question, “Which one of the following is not a prime number?” We learned that 15 is not a prime number, while 23, 29, and 37 are prime numbers. Understanding prime numbers and their properties can enhance our mathematical knowledge and problem-solving abilities.

Q&A

1. 1. What are prime numbers?

Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.

1. 1. How can we identify prime numbers?

One common method to identify prime numbers is the trial division method, where we divide the number by all the numbers less than it and check for any