BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon103 Learners

Last updated on July 1st, 2025

Math Whiteboard Illustration

Prime Numbers 100 to 400

Professor Greenline Explaining Math Concepts

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.

Prime Numbers 100 to 400 for Saudi Students
Professor Greenline from BrightChamps

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.
Professor Greenline from BrightChamps

Prime Numbers 100 to 400 Chart

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.

Professor Greenline from BrightChamps

List of All Prime Numbers 100 to 400

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

Professor Greenline from BrightChamps

Prime Numbers - Odd Numbers

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.

Professor Greenline from BrightChamps

How to Identify Prime Numbers 100 to 400

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.

Professor Greenline from BrightChamps

Rules for Identifying Prime Numbers 100 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 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.
Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in Prime Numbers 100 to 400

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:

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Confusing composite numbers with prime numbers.

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

A prime number has exactly 2 divisors: 1 and the number itself. Remember that composite numbers have more than 2 divisors. For example, 121 is not a prime number because it has more than 2 divisors.

Mistake 2

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Including 1 as a prime number.

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Always remember that primes are greater than 1. 1 is not a prime number because it has only one divisor: itself.

Mistake 3

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Not efficiently using the prime checking method.

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Practice using the Sieve of Eratosthenes method efficiently, or check divisibility by primes up to the square root of the number. For example, while checking the divisibility of 169, stop once you reach √169.

Mistake 4

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Not realizing about the primes in the larger prime range.

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Keep practicing identifying larger primes, as it sharpens students' skills. The Sieve of Eratosthenes method helps solve this.

Mistake 5

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting that multiples of any prime number are not prime.

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Erase all 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.

arrow-right
Max from BrightChamps Saying "Hey"

Prime Numbers Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Is 397 a prime number?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Yes, 397 is a prime number.

Explanation

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.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

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?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

101 is the 3-digit code Carlos should use, as it is the smallest prime number over 100.

Explanation

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.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

A teacher asks her students: Identify the prime number closest to 150.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

149 is the prime number closest to 150.

Explanation

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.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQs on Prime Numbers 100 to 400

1.Give some examples of prime numbers between 100 and 400.

Math FAQ Answers Dropdown Arrow

2.Explain prime numbers in math.

Math FAQ Answers Dropdown Arrow

3.Is 2 the smallest prime number?

Math FAQ Answers Dropdown Arrow

4.Which is the largest prime number in 100 to 400?

Math FAQ Answers Dropdown Arrow

5.Are there infinite prime numbers?

Math FAQ Answers Dropdown Arrow

6.How can children in Saudi Arabia use numbers in everyday life to understand Prime Numbers 100 to 400?

Math FAQ Answers Dropdown Arrow

7.What are some fun ways kids in Saudi Arabia can practice Prime Numbers 100 to 400 with numbers?

Math FAQ Answers Dropdown Arrow

8.What role do numbers and Prime Numbers 100 to 400 play in helping children in Saudi Arabia develop problem-solving skills?

Math FAQ Answers Dropdown Arrow

9.How can families in Saudi Arabia create number-rich environments to improve Prime Numbers 100 to 400 skills?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for Prime Numbers 100 to 400

  • 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.
Math Teacher Background Image
Math Teacher Image

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.

Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom