Prime Numbers: Meaning, How to Find Them, and Practice Questions
Prime numbers are numbers greater than 1, divisible only by 1 and themselves. Learn properties of prime numbers, methods of identification, and test your skills with practice questions.
Chandni 5 Sept, 2025
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Prime Numbers are a unique group of numbers that have specific characteristics. A prime number is a number greater than 1 that can only be divided by 1 and itself without leaving a remainder. For example, 2, 3, 5, and 7 are prime numbers.
These numbers play a significant role in mathematics, as they are the building blocks of all other numbers. Understanding prime numbers helps in solving various mathematical problems and plays a role in many real-world applications.Prime Numbers
Prime numbers are special numbers that have only two divisors, 1 and themselves. They cannot be divided exactly by any other number. For example, 2, 3, 5, and 7 are prime numbers because no number except 1 and the number itself can divide them evenly. If you are still thinking that What are prime numbers? then Prime numbers are the basic building blocks of math.
What is Prime Number?
Want to know What is prime number?, then A prime number is a natural number greater than 1 that can only be divided by 1 and itself without leaving a remainder. This means that the number has exactly two distinct positive divisors. For example, the number 5 is prime because it can only be divided by 1 and 5. On the other hand, the number 6 is not a prime number because it can be divided by 1, 2, 3, and 6. Prime numbers start from 2, which is the smallest and the only even prime number. All subsequent prime numbers are odd, with numbers like 3, 5, 7, 11, 13, and 17 forming the initial sequence of prime numbers.Prime Numbers Meaning
Prime numbers meaning is that these are numbers only divisible by 1 and themselves. They are important in math because every number can be made by multiplying prime numbers. This makes them like the "building blocks" of all numbers.
Prime Number Definition
Prime number definition says it's a positive whole number greater than 1 that has exactly two factors: 1 and the number itself. Unlike composite numbers, prime numbers cannot be formed by multiplying smaller numbers other than 1 and itself.
Prime Numbers Definition and Examples
Prime numbers definition and examples show that prime numbers have exactly two factors: 1 and the number itself. Examples are 2, 3, 5, 7, 11, etc. These numbers cannot be divided evenly by any other number. Numbers like 4, 6, or 8 are not prime because they have more factors.
Prime Numbers vs. Composite Numbers
Prime numbers are distinct from composite numbers. While prime numbers have exactly two divisors, composite numbers have more than two divisors. For example:- Prime: 2, 3, 5, 7, 11, 13, 17
- Composite: 4, 6, 8, 9, 10, 12, 14
Characteristics of Prime Numbers
Prime numbers have unique features that make them stand out from other numbers. These characteristics help us easily identify prime numbers and understand why they are important in mathematics. Here are the most important ones:What is the Smallest Prime Number
What is the smallest prime number? It is 2. It is the only even prime number because all other even numbers can be divided by 2, making them non-prime. So, 2 is unique and starts the list of prime numbers.
How to Find Prime Numbers?
Finding prime numbers can be fun and easy! Here are some simple methods that will help you figure out if a number is prime or not.Trial Division (Checking One by One)
This is the easiest way to find prime numbers. Here's how you do it:- Pick a number that you want to check (for example, 13).
- Try dividing the number by 2, 3, 4, 5, and so on, until you reach the number just before the one you are checking (in this case, 12).
- If none of the divisions give a whole number (with no remainder), then the number is prime !
- Try dividing 13 by 2 → No , it doesn’t work.
- Try dividing 13 by 3 → No , it doesn’t work.
- Try dividing 13 by 4 → No , it doesn’t work.
- Try dividing 13 by 5 → No , it doesn’t work.
- Since no number (other than 1 and 13) divides it evenly, 13 is a prime number !
A Fun List Method
This is a fun way to find lots of prime numbers up to a certain number. Here’s how you do it:- Write down all the numbers starting from 2 to the number you want to check (for example, up to 30).
- Start with 2 and cross out all the numbers that can be divided by 2 (like 4, 6, 8, etc.).
- Next, move to the next number that’s not crossed out (in this case, 3 ). Cross out all the numbers that can be divided by 3 (like 6, 9, 12, etc.).
- Then, move to the next number that’s not crossed out (in this case, 5 ), and cross out all the numbers that can be divided by 5 .
- Keep going until you reach the number you are working with (in this case, 30).
- The numbers that remain uncrossed are prime numbers !
- Start with numbers from 2 to 30: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 .
- Cross out all multiples of 2: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 .
- Cross out all multiples of 3: 6, 9, 12, 15, 18, 21, 24, 27, 30 .
- Cross out all multiples of 5: 10, 15, 20, 25, 30 .
Prime Number Formula
There is a special formula that can give you some prime numbers! The formula is: n² + n + 41 Let’s use this formula with some small numbers:- For n = 0 : 0² + 0 + 41 = 41 (which is prime!)
- For n = 1 : 1² + 1 + 41 = 43 (which is prime!)
- For n = 2 : 2² + 2 + 41 = 47 (which is prime!)
- For n = 3 : 3² + 3 + 41 = 53 (which is prime!)
List of Prime Numbers from 1 to 100
Prime numbers are numbers greater than 1 that can only be divided by 1 and themselves. Below is the list of all the prime numbers from 1 to 100, organized into 5 rows for easier reading:
L ist of Prime Numbers from 1 to 100 |
||||
| Prime Numbers | Prime Numbers | Prime Numbers | Prime Numbers | Prime Numbers |
| 2 | 3 | 5 | 7 | 11 |
| 13 | 17 | 19 | 23 | 29 |
| 31 | 37 | 41 | 43 | 47 |
| 53 | 59 | 61 | 67 | 71 |
| 73 | 79 | 83 | 89 | 97 |
Fun Facts About Prime Numbers
Here are some fun facts about prime numbers:- The first prime number is 2 , which is also the only even prime number.
- Prime numbers are important in math games and puzzles .
- There are infinite prime numbers , which means no matter how big a number is, you can always find another prime number bigger than it!
- Prime numbers help make sure your online information, like passwords or credit card numbers, is safe. They are used in special codes to protect information.
- Just like how LEGO pieces help build amazing structures, prime numbers are like building blocks for all numbers! Every composite number can be broken down into prime numbers. This process is called prime factorization.
Prime Number solved Examples
Let’s solve some problems together to practice identifying prime and composite numbers!Example 1: Is 17 a prime number?
- Try dividing 17 by 2, 3, 4, 5, or 6.
- None of these numbers divide 17 evenly.
Example 2: Is 18 a prime number?
Try dividing 18 by 2, 3, 4, 6, 9, and 18. Since 18 can be divided by more than just 1 and 18, it is not a prime number .Example 3: Is 5 a prime number?
Try dividing 5 by 2, 3, or 4. It can’t be divided evenly by any of those numbers.Prime Number Practice Questions
Here are some challenging questions to test your understanding of prime numbers. Try solving them and see how many you can answer correctly!- Which is the smallest prime number greater than 10?
- Can a prime number be a multiple of 2?
- What is the largest prime number less than 20?
- Is the number 21 a prime number? Why or why not?
- Find the prime numbers between 20 and 40.
- Is the number 17 a prime number?
- Circle the prime numbers in the list: 1, 2, 3, 5, 6, 8, 11, 12, 17, 18
- Which of these numbers are prime: 29, 35, 37, 39?
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Prime Numbers FAQs
Are there prime numbers greater than 100?
Yes, there are prime numbers greater than 100. In fact, there are infinitely many primes, and they keep getting larger as you move along the number line
What is a twin prime?
Twin primes are pairs of prime numbers that differ by exactly 2. Examples include (3, 5), (11, 13), and (17, 19). Twin primes are a fascinating area of number theory.
What is the prime factorization of 12?
The prime factorization of 12 is 2 × 2 × 3. Prime factorization is breaking down a number into prime numbers that multiply together to give the original number.
Can prime numbers be negative?
No, prime numbers are always positive integers greater than 1. Negative numbers cannot be prime because they don’t fit the definition of prime numbers having only two divisors: 1 and the number itself.
Is 100 a prime number?
No, 100 is not a prime number because it can be divided by 1, 2, 4, 5, 10, 20, 25, 50, and 100. It has more than two divisors.
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