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Which of the Following is a Prime Number?

 

Introduction

Prime numbers are a fascinating concept in mathematics. They are numbers that are only divisible by 1 and themselves, with no other factors. In this article, we will explore the concept of prime numbers, discuss their properties, and provide examples to help you understand which of the following numbers are prime.

What is a Prime Number?

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, it has no divisors other than 1 and itself. For example, 2, 3, 5, 7, 11, and 13 are all prime numbers.

Properties of Prime Numbers

Prime numbers have several interesting properties:

  • Prime numbers are always odd, except for the number 2, which is the only even prime number.
  • There are infinitely many prime numbers. This was proven by the ancient Greek mathematician Euclid more than 2,000 years ago.
  • Prime numbers cannot be negative or fractions. They are always positive integers.
  • The prime factorization of a composite number is unique. This means that every composite number can be expressed as a product of prime numbers in only one way.

Which of the Following Numbers are Prime?

Let’s now examine the following numbers and determine which ones are prime:

  1. 17
  2. 25
  3. 31
  4. 40
  5. 47

17

17 is a prime number. It is only divisible by 1 and 17, with no other factors. Therefore, it meets the criteria of a prime number.

25

25 is not a prime number. It is divisible by 1, 5, and 25. Since it has factors other than 1 and itself, it is not a prime number.

31

31 is a prime number. It is only divisible by 1 and 31, making it a prime number.

40

40 is not a prime number. It is divisible by 1, 2, 4, 5, 8, 10, 20, and 40. Since it has factors other than 1 and itself, it is not a prime number.

47

47 is a prime number. It is only divisible by 1 and 47, satisfying the criteria of a prime number.

Summary

In conclusion, a prime number is a natural number greater than 1 that has no divisors other than 1 and itself. Prime numbers have unique properties and are essential in various mathematical applications. In the given list of numbers, 17, 31, and 47 are prime numbers, while 25 and 40 are not. Understanding prime numbers can help in solving mathematical problems, cryptography, and other fields where number theory is applied.

Q&A

1. What is the smallest prime number?

The smallest prime number is 2. It is the only even prime number.

2. Are negative numbers prime?

No, prime numbers are always positive integers. Negative numbers cannot be prime because they have factors other than 1 and themselves.

3. How many prime numbers are there between 1 and 100?

There are 25 prime numbers between 1 and 100. They are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

4. Can prime numbers be fractions?

No, prime numbers cannot be fractions. They are always whole numbers or positive integers.

5. Are there prime numbers larger than 100?

Yes, there are prime numbers larger than 100. Prime numbers continue infinitely, and there is no largest prime number.

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