Last updated on July 1st, 2025
Prime numbers are natural numbers greater than 1, having only two factors: 1 and the number itself. Beyond mathematics, prime numbers are crucial in areas like digital security and cryptography. In this topic, we will explore the prime numbers from 100 to 400.
A prime number is a natural number with no positive factors other than 1 and the number itself. Prime numbers are only divisible by 1 and themselves. 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, helping to identify the prime numbers within a range.
For learners, it becomes easier to understand prime numbers through the chart. The significance of this prime number chart is seen in areas like the foundation of mathematics and the fundamental theorem of arithmetic.
The list of all prime numbers from 100 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 100 to 400 include
Prime numbers and odd numbers are numbers that are only divisible by 1 and the number itself. Except for 2, all prime numbers are odd. Therefore, except for 2, all prime numbers are considered a set of odd numbers.
Prime numbers are natural numbers that can only be divided by 1 and the number itself. Here are two important ways to determine whether a number is prime or not.
To determine if a number is prime, use the divisibility method. 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 if 113 is a prime number,
Step 1: 113 ÷ 2 = 56.5 (remainder ≠ 0)
Step 2: 113 ÷ 3 = 37.66 (remainder ≠ 0)
Step 3: 113 ÷ 5 = 22.6 (remainder ≠ 0)
Since no divisors are found, 113 is a prime number.
Prime factorization involves breaking down a composite number into the product of its prime factors. The method of prime factorization helps identify 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, divide 200, 200 ÷ 2 = 100
Step 3: Now take 100, 100 ÷ 2 = 50
Step 4: Take 50, 50 ÷ 2 = 25
Step 5: Take 25, since 25 ends in 5, divide it by 5 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, with no divisors other than 1 and the number itself. In the divisibility check rule, we verify if a number is divisible by 2, 3, 5, or 7. If it is, then it is not a prime number.
Rule 2: Prime Factorization: In this method, we break down all numbers into their prime factors, expressing them as the product of prime numbers.
Rule 3: Sieve of Eratosthenes Method: This ancient algorithm is used to find all prime numbers up to a given limit. First, list all numbers from 100 to 400. Begin with the first prime number, 2, and 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.
While working with the prime numbers 100 to 400, students 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 ≈ 19.92.
We check divisibility by primes less than 19.92 (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.
Carlos is trying to secure his data with a 3-digit prime number. The code should be the smallest prime number over 100. Which prime number should he use?
101 is the 3-digit code Carlos should use, as it is the smallest prime number over 100.
Prime numbers are natural numbers greater than 1 that have no divisors other than 1 and themselves. The smallest prime number over 100 is 101.
A teacher asks her students: Identify the prime number closest to 150.
149 is the prime number closest to 150.
149 is a prime number because it is only divisible by 1 and itself. The next prime number after 149 is 151, which is greater than 150.
Therefore, the prime number closest to 150 is 149.
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.