Last updated on July 2nd, 2025
The natural numbers greater than 1 are called prime numbers. Prime numbers have only two factors, 1 and the number itself. Besides math, we use prime numbers in many fields, such as securing digital data, radio frequency identification, etc. In this topic, we will learn about the prime numbers 301 to 400.
A prime number is a natural number with no positive factors other than 1 and the number itself. A prime number can only be evenly divisible by 1 and the number itself. Here are some basic properties of prime numbers:
A prime number chart is a table showing the prime numbers in increasing order. The chart simply includes all the prime numbers within a certain limit for identifying the prime numbers within a range.
For kids, it will be less difficult to understand the prime numbers through the chart. The significance of this prime number chart is used in different fields like the foundation of mathematics and the fundamental theorem of arithmetic.
The list of all prime numbers from 301 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 301 to 400 include 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, and 397.
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, which divides all the non-prime numbers. Therefore, except 2, all prime numbers are considered a set of odd numbers.
Prime numbers are a set of natural numbers that can only be divided by 1 and the number itself. Here are the two important ways to find whether a number is prime or not.
To find whether a number is prime or not, we use the divisibility method to check. If a number is divisible by 2, 3, or 5, then it will result in a non-prime number. Prime numbers are only divisible by 1 and itself, so if a number is divisible by the number itself and 1, it is a prime number.
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.
The prime factorization method is the process of breaking down a composite number into the product of its prime factors. The method of prime factorization helps to identify the prime numbers up to 400 by building the smallest blocks of any given number.
For example: The prime factorization of 400: Let's break it down into the smallest prime numbers until it can’t divide anymore.
Step 1: 400 ÷ 2 = 200
Step 2: Now, we divide 200, 200 ÷ 2 = 100
Step 3: Now take 100, 100 ÷ 2 = 50
Step 4: Take 50, 50 ÷ 2 = 25
Step 5: Take 25, 25 ÷ 5 = 5
Step 6: At last, take 5. 5 ÷ 5 = 1 (since 5 is a prime number, and dividing by 5 gives 1)
Therefore, the prime factorization of 400 is: 400 = 2^4 × 5^2.
Rule 1: Divisibility Check: Prime numbers are natural numbers that are greater than 1 and have 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, and 7. If it's divisible by these numbers, then it's not a prime number.
Rule 2: Prime Factorization: In this prime factorization method, we break down all the numbers into their prime factors, showing them as the product of prime numbers.
Rule 3: Sieve of Eratosthenes Method: The method of Sieve of Eratosthenes is an ancient algorithm used to find all prime numbers up to a given limit. First, we list all the numbers from 301 to 400. Then start with the first prime number, 2. Mark all the 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 301 to 400
While working with the prime numbers 301 to 400, children might encounter some errors or difficulties. We have many solutions to resolve those problems. Here are some given below:
Is 373 a prime number?
Yes, 373 is a prime number.
The square root of 373 is √373 ≈ 19.31, we check divisibility by primes less than 19.31. (2, 3, 5, 7, 11, 13, 17, 19).
373 ÷ 2 = 186.5
373 ÷ 3 = 124.33
373 ÷ 5 = 74.6
373 ÷ 7 = 53.29
373 ÷ 11 = 33.91
Since 373 is not divisible by any of these numbers, 373 is a prime number.
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.
Prime numbers are natural numbers that are greater than 1 and have 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.
A teacher challenges her students: Find the prime numbers that are closest to 350 but less than 350.
349 is the prime number that is closest to 350.
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.
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.