107 LearnersLast updated on June 9th, 2025
Prime Numbers 1 to 500
The natural numbers greater than 1 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, etc. In this topic, we will learn about the prime numbers 1 to 500.
Prime Numbers 1 to 500
A prime number is a natural number with no positive factors other than 1 and the number itself. And the 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 is greater than 2 and 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 number.
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Prime Numbers 1to 500 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 less difficult 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, fundamental theorem of arithmetic.
List of All Prime Numbers 1 to 500
The list of all prime numbers from 1 to 500 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 1 to 500 include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499.
Prime Numbers - Odd Numbers
Prime numbers and odd numbers are the numbers that are only divisible by 1 and the number itself. It 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 2 all prime numbers are considered as the set of odd numbers.
How to Identify Prime Numbers 1 to 500
Prime numbers are a set of natural numbers that can only be divided by 1 and the number itself. Here are the two important ways to find 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, or 5 then it will result in a non-prime number. Prime numbers are only divisible by 1 and itself, so if a number is divisible by the number itself and 1 is meant to be a prime number. For example:
To check whether 29 is a prime number,
Step 1: 29 ÷ 2 = 14.5 (remainder ≠ 0)
Step 2: 29 ÷ 3 = 9.66 (remainder ≠ 0)
Step 3: 29 ÷ 5 = 5.8 (remainder ≠ 0)
Since no divisors are found, 29 is a prime number.
By Prime Factorization Method
The Prime factorization method is the process of breaking down the composite number into the product of its prime factors. The method of prime factorization helps to identify the prime numbers up to 500 by building the smallest blocks of any given number. For example:
The prime factorization of 500: Let's break it down into the smallest prime numbers until it can’t divide anymore.
Step 1: 500 ÷ 2 = 250
Step 2: Now, we divide 250,
250 ÷ 2 = 125
Step 3: Now take 125, since 125 ends in 5 divide the number with 5
125 ÷ 5 = 25
Step 4: Take 25, since 25 ends in 5 divide the number with 5
25 ÷ 5 = 5
Step 5: At last, take 5.
5 ÷ 5 = 1 (since 5 is a prime number, and dividing by 5 gives 1)
Therefore, the prime factorization of 500 is: 500 = 22 × 53.
Rules for Identifying Prime Numbers 1 to 500
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 2, 3, 5, and 7. If it's divisible by these numbers then it's not a prime number.
Rule 2: Prime Factorization: In this prime factorization 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 500. Then start with the first prime number, 2. Mark all the multiples of 2 as non-prime. Repeat the process for the next unmarked prime number and continue until you reach the square root of 500 approximately 22.36. The remaining unmarked numbers are the prime numbers.
Tips and Tricks for Prime Numbers 1 to 500
- Use common shortcuts to memorize the prime numbers. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 use these numbers as reference.
- Practice using the method of Sieve Eratosthenes efficiently.
- Numbers like 4, 8, 9, 16, 25, 36 are never meant to prime. Knowing the common powers of numbers helps in avoiding unnecessary checks.
Common Mistakes and How to Avoid Them in Prime Numbers 1 to 500
While working with the prime numbers 1 to 500 children might encounter some errors or difficulties. We have many 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: 9 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 Eratosthenes efficiently, or check divisibility by primes up to the square root of the number.
For example: while checking the divisibility of 121 stop once you reach √121.
Mistake 4
Not realizing about the primes in the larger prime range.
Keep on practicing identifying the larger primes, as it helps to sharpen the skills of children. The usage of the method of Sieve Eratosthenes helps to solve this.
Mistake 5
Forgetting about multiples of any prime number is not prime.
Erase all the multiples of known prime numbers as soon as possible.
For example: If you're checking numbers up to 500, you don't have to check numbers divisible by 2,3,5, or 7 because they are not prime.
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Prime Numbers Examples
Problem 1
Is 499 a prime number?
Yes, 499 is a prime number.
Explanation
The square root of 499 is √499 = 22.33, we check divisibility by primes less than 22.33. (2, 3, 5, 7, 11, 13, 17, 19).
499 ÷ 2 = 249.5
499 ÷ 3 = 166.33
499 ÷ 5 = 99.8
499 ÷ 7 = 71.28
499 ÷ 11 = 45.364
Since 499 is not divisible by any of these numbers, 499 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 500. Which prime number will open the lock?
499 is the 3-digit code of the digital locker and the largest prime number under 500.
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 500 are 2, 3, 5, 7, 11, 13, and so on.
499 is the largest prime number under 500, therefore the code to open the digital locker is 499.
Problem 3
A teacher challenges her students: Find the prime numbers that are closest to 60 but less than 60.
59 is the prime number which is closest to 60.
Explanation
59 is a prime number because it is only divisible by 1 and the number itself.
And the next prime number after 59 is 61, which is greater than 60.
Therefore, the prime number closest to 60 and less than 60 is 59.
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FAQs on Prime Numbers 1 to 500
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 in 1 to 500?
6.How can children in Vietnam use numbers in everyday life to understand Prime Numbers 1 to 500?
7.What are some fun ways kids in Vietnam can practice Prime Numbers 1 to 500 with numbers?
8.What role do numbers and Prime Numbers 1 to 500 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Prime Numbers 1 to 500 skills?
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Important Glossaries for Prime Numbers 1 to 500
- Prime numbers: The natural numbers which are greater than 1 and that are divisible by 1 and the number itself. For example: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 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: 3, 5, 7, 9, 11, 13, and so on.
- Composite numbers: Composite numbers are non-prime numbers that have more than 2 factors. For example, 12 is a composite number, and it is divisible by 1, 2, 3, 4, 6, and 12.
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.
