## Introduction

Prime numbers have always fascinated mathematicians and enthusiasts alike. They are the building blocks of the number system, possessing unique properties that make them intriguing. In this article, we will explore the question: Is 73 a prime number? We will delve into the definition of prime numbers, examine the divisibility rules, and provide evidence to determine whether 73 is indeed a prime number or not.

## Understanding Prime Numbers

Before we dive into the specifics of 73, let’s first establish 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 evenly divided by any other number except 1 and itself.

## Divisibility Rules

To determine whether a number is prime or not, we can apply various divisibility rules. These rules help us identify if a number is divisible by another number without performing the actual division.

### Divisibility by 2

Even numbers are divisible by 2. Since 73 is an odd number, it is not divisible by 2. Therefore, we can conclude that 73 is not divisible by 2.

### Divisibility by 3

To check if a number is divisible by 3, we can sum its digits. If the sum is divisible by 3, then the number itself is divisible by 3. Let’s apply this rule to 73: 7 + 3 = 10. Since 10 is not divisible by 3, we can conclude that 73 is not divisible by 3.

### Divisibility by 5

Numbers ending in 0 or 5 are divisible by 5. Since 73 does not end in 0 or 5, it is not divisible by 5.

### Divisibility by 7

Divisibility by 7 is a bit more complex. We can subtract twice the last digit from the remaining truncated number. If the result is divisible by 7, then the original number is divisible by 7. Let’s apply this rule to 73: 73 – (2 * 3) = 73 – 6 = 67. Since 67 is not divisible by 7, we can conclude that 73 is not divisible by 7.

## Is 73 a Prime Number?

Based on the divisibility rules we have applied, we can confidently state that 73 is not divisible by 2, 3, 5, or 7. This leads us to believe that 73 might indeed be a prime number. However, to confirm this, we need to conduct further analysis.

### Factors of 73

To determine if 73 is a prime number, we need to find its factors. Factors are the numbers that divide a given number without leaving a remainder. If a number has only two factors (1 and itself), then it is a prime number.

Let’s find the factors of 73:

- 1
- 73

As we can see, 73 has only two factors: 1 and 73. Therefore, we can conclude that 73 is indeed a prime number.

## Examples of Prime Numbers

Now that we have established that 73 is a prime number, let’s explore some other examples of prime numbers:

- 2: The smallest prime number.
- 5: A prime number that ends in 5.
- 11: A prime number that is not divisible by any other number.
- 97: A prime number that is close to 100.

These examples demonstrate the diversity and uniqueness of prime numbers.

## Conclusion

In conclusion, after applying the divisibility rules and analyzing the factors, we can confidently state that 73 is indeed a prime number. Prime numbers, like 73, possess special properties that make them fascinating to mathematicians and enthusiasts. They play a crucial role in various mathematical concepts and applications. Understanding prime numbers helps us unravel the mysteries of the number system and appreciate the beauty of mathematics.

## Q&A

### Q1: What is a prime number?

A1: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

### Q2: What are some other examples of prime numbers?

A2: Some other examples of prime numbers include 2, 5, 11, and 97.

### Q3: How can we determine if a number is prime?

A3: We can determine if a number is prime by applying divisibility rules and analyzing its factors.

### Q4: Are there infinitely many prime numbers?

A4: Yes, there are infinitely many prime numbers. This was proven by the ancient Greek mathematician Euclid over 2,000 years ago.

### Q5: Can prime numbers be negative?

A5: No, prime numbers are defined as natural numbers greater than 1. Negative numbers and 0 are not considered prime.