Last updated on July 1st, 2025
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.
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:
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.
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 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 two important ways to determine 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, 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.
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.
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.
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:
Is 997 a prime number?
Yes, 997 is a prime number.
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.
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.
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.
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.
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.
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.