Last updated on July 1st, 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 1 to 400.
A prime number is a natural number with no positive factors other than 1 and the number itself. The 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 includes all the prime numbers up to 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 1 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 1 to 400 include:
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 for 2, all prime numbers are considered as the 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 only the number itself and 1, it is considered a prime number.
For example: To check whether 37 is a prime number,
Step 1: 37 ÷ 2 = 18.5 (remainder ≠ 0)
Step 2: 37 ÷ 3 = 12.33 (remainder ≠ 0)
Step 3: 37 ÷ 5 = 7.4 (remainder ≠ 0)
Since no divisors are found, 37 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: Finally, 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 = 24 × 52.
Rule 1: Divisibility Check: Prime numbers are natural numbers greater than 1 and have no divisors other than 1 and the number itself. In the divisibility check rule, we check whether the prime number is divisible by 2, 3, 5, or 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, 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 1 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, which is 20. The remaining unmarked numbers are the prime numbers.
Use common shortcuts to memorize the prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and use these numbers as references. Practice using the method of Sieve of Eratosthenes efficiently. Numbers like 4, 8, 9, 16, 25, 36 are never prime. Knowing the common powers of numbers helps in avoiding unnecessary checks.
While working with the prime numbers 1 to 400, children might encounter some errors or difficulties. We have many solutions to resolve those problems. Here are some given below:
Is 397 a prime number?
Yes, 397 is a prime number.
The square root of 397 is √397 ≈ 19.93, we check divisibility by primes less than 19.93 (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
397 ÷ 13 = 30.53
397 ÷ 17 = 23.35
397 ÷ 19 = 20.89
Since 397 is not divisible by any of these numbers, 397 is a prime number.
John is trying to unlock a treasure box with a 3-digit number. The code is the largest prime number under 400. Which prime number will open the box?
The code to open the treasure box is 397, the largest prime number under 400.
Prime numbers are natural numbers greater than 1 and have no divisors other than 1 and the number itself. The prime numbers under 400 are 2, 3, 5, 7, 11, 13, and so on. 397 is the largest prime number under 400; therefore, the code to open the treasure box is 397.
A teacher challenges her students: Find the prime numbers that are closest to 50 but less than 50.
47 is the prime number which is closest to 50.
47 is a prime number because it is only divisible by 1 and the number itself. The next prime number after 47 is 53, which is greater than 50. Therefore, the prime number closest to 50 and less than 50 is 47.
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.