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Last updated on September 29, 2025
Do you know what prime numbers are? They are numbers that have exactly two factors: 1 and the number itself. They cannot be written as the product of two distinct positive integers. In this article, let’s explore what prime numbers are.
A prime number is defined as any positive number that can be divided only by itself and 1. They are one of the most essential building blocks of mathematics. Prime numbers are used in decryption and encryption software, rotor machines, telecommunication codes, and hash tables to organize and display the data. For example, consider the prime number 7. It only has two divisors: 1 and 7. 7 ÷ 2 = 3.5, with a remainder of 1. Here, dividing a prime number by any other natural number results in other leftover numbers.
Numbers can sometimes be either classified as prime or composite based on their factors.
Prime number |
Composite number |
Natural numbers are greater than one and have only two factors that are one and the number itself. |
Natural numbers greater than one and have more than two factors. |
Prime numbers cannot be written as the product of two smaller integers.
For example: 5 = 5 × 1 |
The numbers that can be expressed as the product of prime numbers are composite numbers.
For example: 12 = 2 × 2 × 3 = 22 × 3 |
The numbers which are only divisible by 1 and the number itself are prime numbers.
Example: 11 is only divisible by 1 and 11. |
Composite numbers have more than two factors.
Example: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24 |
Examples: 2, 3, 5, 7, 11, etc. |
Examples: 4, 6, 8, 10, 12, etc. |
A pair of prime numbers where the difference between them is two is known as twin primes. In between a pair of twin primes, there is a composite number. For example, (3, 5), (5, 7), (11, 13), (17, 19), and so on.
Co-primes are a pair of numbers where the common factor of the two numbers is 1. In co-primes, one number can be prime, and the other can be a composite number. Here, the only condition is that the common factor should be 1. For example, (2, 3), (5, 9), (9, 10), and so on.
Any composite number can be expressed as the product of its prime factors. This process is known as prime factorization. For example, the prime factorization of 34 is 2 × 17; here, 2 and 17 are the prime factors of 34.
Confused about how to learn and master prime numbers? When learning prime numbers, try to follow these tips and tricks to master them. These tricks can help you learn prime numbers quickly.
When learning about prime numbers, students make errors that they tend to repeat. To learn and master prime numbers, let’s discuss some common mistakes and how to avoid them.
In our daily lives, we use prime numbers in various fields, such as cryptography and data security, as well as in analyzing number patterns and other applications. Let’s learn a few real-world applications of prime numbers.
Cryptography and data security: Prime numbers are used in encryption algorithms through public-key cryptography, such as RSA. Cryptography is used to decrypt or encrypt data. For data security, prime numbers can be used as passwords.
Simplification of fractions: Prime numbers can be used to find the GCF of more than two numbers. GCF is used to simplify the fractions.
Analyzing number patterns: As prime numbers are considered the building blocks of all integers, they help understand the relationship between numbers. We use prime numbers in hash tables to distribute the data key evenly.
What is the sum of the first five prime numbers?
The sum of the first five prime numbers is 28.
The first five prime numbers are 2, 3, 5, 7, 11.
Sum of first five prime numbers = 2 + 3 + 5 + 7 + 11 = 28
How many primes are there between 2 and 20
The prime numbers between 2 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19.
The prime numbers are the numbers which are only divisible by 1 and the number itself.
So the prime numbers between 2 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19.
If x is a prime number, how many factors does x^2 have?
If x is a prime number, x2 has 3 factors.
Here, x is a prime number
So, the factors of x are 1 and x
The factors of x2 are 1, x, and x2
Therefore, the number of factors of x2 is 3.
Which of the following is not a prime number: 83, 101, 105, 89, 11.
105 is not a prime number.
The factors of 83, 101, 89, and 11 are 1, and the number itself.
Meanwhile, the factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105.
Therefore, 105 is not a prime number.
Which is the greatest prime number between 11 and 30?
The greatest prime number between 11 and 30 is 29.
The prime numbers between 11 and 30 are 11, 13, 17, 19, 23, and 29.
So the greatest prime number is 29.
Is 97 a prime number?
Yes, 97 is a prime number.
The factors of 97 are 1 and 97, so it is only divisible by 1 and 97.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.