Prime Numbers 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:

• 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 (Goldbach's conjecture).

• 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.

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.

By Divisibility Method:

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.

By Prime Factorization Method:

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.

Tips and Tricks for Prime Numbers 100 to 400

• Use common shortcuts to memorize the prime numbers. 101, 103, 107, 109, 113, 127, 131, 137, 139, 149

• use these numbers as references. Practice using the Sieve of Eratosthenes method efficiently.

• Numbers like 104, 108, 110, 116, 124, 136 are never prime. Knowing the common powers of numbers helps avoid unnecessary checks.

• Prime numbers: Natural numbers greater than 1, divisible only by 1 and the number itself. For example, 101, 103, 107, 109, and so on.

• Odd numbers: Numbers not divisible by 2. All prime numbers except 2 are odd. For example, 3, 5, 7, 9, 11, 13, and so on.

• Composite numbers: Non-prime numbers that have more than 2 factors. For example, 12 is a composite number, divisible by 1, 2, 3, 4, 6, and 12.

• Divisibility method: A technique to check whether a number is prime by checking its divisibility by smaller prime numbers.

• Sieve of Eratosthenes: An ancient algorithm for finding all prime numbers up to a specified integer limit, by iteratively marking the multiples of each prime number.