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102 LearnersLast updated on August 30, 2025
Prime Numbers 300 to 400
Natural numbers greater than 1 are called prime numbers. Prime numbers have only two factors, 1 and the number itself. Beyond mathematics, prime numbers are used in various fields such as securing digital data, radio frequency identification, etc. In this topic, we will learn about the prime numbers from 300 to 400.
Prime Numbers 300 to 400
A prime number is a natural number with no positive factors other than 1 and the number itself. Prime numbers can only be evenly divisible by 1 and the number itself. Here are some basic properties of prime numbers:
Every number greater than 1 is divisible by at least one prime number.
Two prime numbers are always relatively prime to each other.
Every even positive integer greater than 2 can be written as the sum of two prime numbers.
Every composite number can be uniquely factored into prime factors.
Except for 2, all prime numbers are odd; 2 is the only even prime number.
Prime Numbers 300 to 400 Chart
A prime number chart is a table showing the prime numbers in increasing order.
The chart includes all the prime numbers within a certain range to help identify prime numbers.
For children, understanding prime numbers through the chart can be simpler.
This prime number chart is significant in various fields like the foundation of mathematics and the fundamental theorem of arithmetic.
List of All Prime Numbers 300 to 400
The list of all prime numbers from 300 to 400 provides a comprehensive view of numbers in this range that can only be divided by 1 and the number itself.
The prime numbers in the range of 300 to 400 include: 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, and 397.
Prime Numbers - Odd Numbers
Prime numbers and odd numbers are numbers that are only divisible by 1 and the number itself.
They cannot be evenly divisible by 2 or other numbers. 2 is the only even prime number.
Therefore, except for 2, all prime numbers are considered a set of odd numbers.
How to Identify Prime Numbers 300 to 400
Prime numbers are a set of natural numbers that can only be divided by 1 and the number itself. Here are two important ways to find whether a number is prime or not.
By Divisibility Method:
To determine if a number is prime, we use the divisibility method to check. If a number is divisible by 2, 3, or 5, then it is not a prime number. Prime numbers are only divisible by 1 and themselves. For example: To check whether 311 is a prime number,
Step 1: 311 ÷ 2 = 155.5 (remainder ≠ 0)
Step 2: 311 ÷ 3 = 103.67 (remainder ≠ 0)
Step 3: 311 ÷ 5 = 62.2 (remainder ≠ 0)
Since no divisors are found, 311 is a prime number.
By Prime Factorization Method:
The prime factorization method breaks down a composite number into the product of its prime factors. This method helps identify prime numbers up to 400 by building the smallest blocks of any given number. For example: The prime factorization of 360: Let's break it down into the smallest prime numbers until it can’t divide anymore.
Step 1: 360 ÷ 2 = 180
Step 2: Now, divide 180, 180 ÷ 2 = 90
Step 3: Now take 90, 90 ÷ 2 = 45
Step 4: Take 45, 45 ÷ 3 = 15
Step 5: Take 15, 15 ÷ 3 = 5
Step 6: Finally, take 5, 5 ÷ 5 = 1 (since 5 is a prime number, and dividing by 5 gives 1)
Therefore, the prime factorization of 360 is: 360 = 23 × 32 × 5.
Rules for Identifying Prime Numbers 300 to 400
Rule 1: Divisibility Check:
Prime numbers are natural numbers greater than 1 with no divisors other than 1 and the number itself. In the divisibility check rule, we check whether the number is divisible by 2, 3, 5, or 7. If it is divisible by these numbers, it is not a prime number.
Rule 2: Prime Factorization:
In this method, we break down all numbers into their prime factors, showing them as the product of prime numbers.
Rule 3: Sieve of Eratosthenes Method:
The sieve of Eratosthenes is an ancient algorithm used to find all prime numbers up to a given limit. First, list all numbers from 300 to 400. Start with the first prime number, 2. Mark all multiples of 2 as non-prime. Repeat the process for the next unmarked prime number and continue until you reach the square root of 400, approximately 20. The remaining unmarked numbers are the prime numbers.
Tips and Tricks for Prime Numbers 300 to 400
Use common shortcuts to memorize the prime numbers: 307, 311, 313, 317, 331, 337, 347.
Practice using the method of Sieve of Eratosthenes efficiently.
Numbers like 304, 306, 312, 324, 338 are never prime.
Knowing the common multiples helps avoid unnecessary checks.
Common Mistakes and How to Avoid Them in Prime Numbers 300 to 400
While working with the prime numbers 300 to 400, children might encounter some errors or difficulties. Here are some solutions to resolve those problems:
Mistake 1
Confusing composite numbers with prime numbers.
A prime number has exactly 2 divisors: 1 and the number itself. Remember that composite numbers have more than 2 divisors.
For example: 333 is not a prime number because it has more than 2 divisors.
Mistake 2
Including 1 as a prime number.
Always remember that primes are greater than 1. 1 is not a prime number because it has only one divisor, itself.
Mistake 3
Not efficiently using the prime checking method.
Practice using the method of Sieve of Eratosthenes efficiently, or check divisibility by primes up to the square root of the number.
For example: while checking the divisibility of 361, stop once you reach √361.
Mistake 4
Not realizing about the primes in the larger prime range.
Keep practicing identifying the larger primes, as it helps to sharpen the skills of children. The use of the Sieve of Eratosthenes method helps to solve this.
Mistake 5
Forgetting about multiples of any prime number is not prime.
Erase all the multiples of known prime numbers as soon as possible.
For example: If you're checking numbers up to 400, you don't have to check numbers divisible by 2, 3, 5, or 7 because they are not prime.
Prime Numbers Examples
Problem 1
Is 397 a prime number?
Yes, 397 is a prime number.
Explanation
The square root of 397 is √397 ≈ 19.9, we check divisibility by primes less than 19.9 (2, 3, 5, 7, 11, 13, 17, 19).
397 ÷ 2 = 198.5
397 ÷ 3 = 132.33
397 ÷ 5 = 79.4
397 ÷ 7 = 56.71
397 ÷ 11 = 36.09
Since 397 is not divisible by any of these numbers, 397 is a prime number.
Problem 2
Annie is trying to open a digital locker with a 3-digit number. The code is the largest prime number under 400. Which prime number will open the lock?
397 is the 3-digit code of the digital locker and the largest prime number under 400.
Explanation
Prime numbers are natural numbers greater than 1 with no divisors other than 1 and the number itself.
The prime numbers under 400 are 307, 311, 313, and so on.
397 is the largest prime number under 400, therefore the code to open the digital locker is 397.
Problem 3
A teacher challenges her students: Find the prime number that is closest to 350 but less than 350.
349 is the prime number that is closest to 350.
Explanation
349 is a prime number because it is only divisible by 1 and the number itself.
The next prime number after 349 is 353, which is greater than 350.
Therefore, the prime number closest to 350 and less than 350 is 349.
FAQs on Prime Numbers 300 to 400
1.Give some examples of prime numbers.
2.Explain prime numbers in math.
3.Is 2 the smallest prime number?
4.Which is the largest prime number?
5.Which is the largest prime number between 300 to 400?
Important Glossary for Prime Numbers 300 to 400
- Prime numbers: Natural numbers greater than 1 that are divisible by only 1 and the number itself. For example: 307, 311, 313, 317, 331, and so on.
- Odd numbers: Numbers that are not divisible by 2. All prime numbers except 2 are odd. For example: 307, 311, 313, 317, 331, and so on.
- Composite numbers: Non-prime numbers that have more than 2 factors. For example, 360 is a composite number and is divisible by 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
- Divisibility: A concept of dividing one number by another and checking if the remainder is zero.
- Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a given limit.
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Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
