103 LearnersLast updated on July 1st, 2025
Prime Numbers 100 to 1000
The natural numbers greater than 1 that are not divisible by any other number except 1 and the number itself 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, and more. In this topic, we will learn about the prime numbers from 100 to 1000.
Prime Numbers 100 to 1000
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:
- 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.
- 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.
Prime Numbers 100 to 1000 Chart
A prime number chart is a table showing the prime numbers in increasing order. The chart simply includes all the prime numbers up to a certain limit for identifying the prime numbers within a range.
For kids, it will be easier 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.
List of All Prime Numbers 100 to 1000
The list of all prime numbers from 100 to 1000 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 1000 include
Prime Numbers - Odd Numbers
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.
How to Identify Prime Numbers 100 to 1000
Prime numbers are a set of 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 find whether a number is prime or not, we use the divisibility method to check. If a number is divisible by 2, 3, 5, or other small primes, then it is not a prime number. Prime numbers are only divisible by 1 and themselves, so if a number is divisible by the number itself and 1, it is a prime number.
For example: To check whether 137 is a prime number,
Step 1: 137 ÷ 2 = 68.5 (remainder ≠ 0)
Step 2: 137 ÷ 3 ≈ 45.67 (remainder ≠ 0)
Step 3: 137 ÷ 5 = 27.4 (remainder ≠ 0)
Since no divisors are found, 137 is a prime number.
By Prime Factorization Method:
The prime factorization method involves breaking down a composite number into the product of its prime factors. The method of prime factorization helps identify the prime numbers up to 1000 by building the smallest blocks of any given number.
For example: The prime factorization of 1000: Break it down into the smallest prime numbers until it can’t divide anymore.
Step 1: 1000 ÷ 2 = 500
Step 2: Now, divide 500, 500 ÷ 2 = 250
Step 3: Now take 250, 250 ÷ 2 = 125
Step 4: Take 125, since 125 ends in 5, divide the number by 5 ,125 ÷ 5 = 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 1000 is: 1000 = 23 × 53.
Rules for Identifying Prime Numbers 100 to 1000
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 prime number is divisible by small primes like 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 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 1000. Then start with the first prime number, 2. 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 1000, approximately 31.62. The remaining unmarked numbers are the prime numbers.
Tips and Tricks for Prime Numbers 100 to 1000
- Use common shortcuts to memorize the prime numbers. 101, 103, 107, 109, 113, 127, 131, 137, 139 use these numbers as references.
- Practice using the method of Sieve of Eratosthenes efficiently. Numbers like 100, 144, 225, 400, 625, 900 are never prime.
- Knowing the common powers of numbers helps in avoiding unnecessary checks.
Common Mistakes and How to Avoid Them in Prime Numbers 100 to 1000
While working with the prime numbers 100 to 1000, children might encounter some errors or difficulties. We have solutions to resolve those problems. Here are some given below:
Mistake 1
Confusing composite numbers with prime numbers.
A prime number has exactly 2 divisors: 1 and the number itself. Remember that composite numbers have more than 2 divisors. For example: 117 is not a prime number because it has more than 2 divisors.
Mistake 2
Including 1 as a prime number.
Always remember that primes are greater than 1. 1 is not a prime number because it has only one divisor itself.
Mistake 3
Not efficiently using the prime checking method.
Practice using the method of Sieve of Eratosthenes efficiently, or check divisibility by primes up to the square root of the number. For example: while checking the divisibility of 289, stop once you reach √289.
Mistake 4
Not realizing about the primes in the larger prime range.
Keep practicing identifying the larger primes, as it helps to sharpen the skills of children. The usage of the method of Sieve of Eratosthenes helps solve this.
Mistake 5
Forgetting that multiples of any prime number are not prime.
Erase all the multiples of known prime numbers as soon as possible. For example: If you're checking numbers up to 1000, you don't have to check numbers divisible by 2, 3, 5, 7, or 11 because they are not prime.
Prime Numbers Examples
Problem 1
Is 997 a prime number?
Yes, 997 is a prime number.
Explanation
The square root of 997 is √997 ≈ 31.56, we check divisibility by primes less than 31.56. (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31).
997 ÷ 2 = 498.5
997 ÷ 3 ≈ 332.33
997 ÷ 5 = 199.4
997 ÷ 7 ≈ 142.43
997 ÷ 11 ≈ 90.64
Since 997 is not divisible by any of these numbers, 997 is a prime number.
Problem 2
Annie is trying to open a digital locker with a 3-digit number. The code is the largest prime number under 1000. Which prime number will open the lock?
997 is the 3-digit code of the digital locker and the largest prime number under 1000.
Explanation
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 1000 are 101, 103, 107, and so on. 997 is the largest prime number under 1000, therefore the code to open the digital locker is 997.
Problem 3
A teacher challenges her students: Find the prime numbers that are closest to 150 but less than 150.
149 is the prime number which is closest to 150.
Explanation
149 is a prime number because it is only divisible by 1 and the number itself. The next prime number after 149 is 151, which is greater than 150. Therefore, the prime number closest to 150 and less than 150 is 149.
FAQs on Prime Numbers 100 to 1000
1.Give some examples of prime numbers.
2.Explain prime numbers in math.
3.Is 2 the smallest prime number?
4.Which is the largest prime number?
5.Which is the largest prime number from 100 to 1000?
6.How can children in Vietnam use numbers in everyday life to understand Prime Numbers 100 to 1000?
7.What are some fun ways kids in Vietnam can practice Prime Numbers 100 to 1000 with numbers?
8.What role do numbers and Prime Numbers 100 to 1000 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Prime Numbers 100 to 1000 skills?
Important Glossaries for Prime Numbers 100 to 1000
- Prime numbers: The natural numbers which are greater than 1 and are divisible by only 1 and the number itself. For example: 101, 103, 107, 109, 113, 127, 131, 137, 139, and so on.
- Odd numbers: The numbers that are not divisible by 2 are called odd numbers. All prime numbers except 2 are odd. For example: 101, 103, 107, 109, and so on.
- Composite numbers: Composite numbers are non-prime numbers that have more than 2 factors. For example, 100 is a composite number, and it is divisible by 1, 2, 4, 5, 10, 20, 25, 50, and 100.
- Divisibility: The ability of one number to be divided by another without leaving a remainder. For example, 100 is divisible by 2, 4, 5, and 10.
- Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a given limit by iteratively marking the multiples of each prime number starting from 2.
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.
Fun Fact
: She loves to read number jokes and games.
