Last updated on June 30th, 2025
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 31.
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:
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 and the fundamental theorem of arithmetic.
The list of all prime numbers from 1 to 31 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 31 include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.
Prime numbers and odd numbers are the numbers that are only divisible by 1 and the number itself. Except for 2, which is the only even prime number, all other prime numbers are odd.
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 any number other than 1 and itself, it is not a prime number.
For example: To check whether 17 is a prime number,
Step 1: 17 ÷ 2 = 8.5 (remainder ≠ 0)
Step 2: 17 ÷ 3 = 5.66 (remainder ≠ 0)
Step 3: 17 ÷ 5 = 3.4 (remainder ≠ 0)
Since no divisors are found, 17 is a prime number. -
The prime factorization method is the process of breaking down the composite number into the product of its prime factors. For example: The prime factorization of 30: Let's break it down into the smallest prime numbers until it can’t divide anymore.
Step 1: 30 ÷ 2 = 15
Step 2: Now, we divide 15, 15 ÷ 3 = 5
Step 3: At last, take 5. 5 ÷ 5 = 1
Therefore, the prime factorization of 30 is: 30 = 2 × 3 × 5.
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.
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: This ancient algorithm is used to find all prime numbers up to a given limit.
Repeat the process for the next unmarked prime number and continue until you reach the square root of 31, approximately 5.57. The remaining unmarked numbers are the prime numbers.
While working with the prime numbers 1 to 31, children might encounter some errors or difficulties. Here are some solutions to resolve those problems:
Is 29 a prime number?
Yes, 29 is a prime number.
The square root of 29 is √29 = 5.38,
so we check divisibility by primes less than 5.38 (2, 3, 5).
29 ÷ 2 = 14.5
29 ÷ 3 = 9.66
29 ÷ 5 = 5.8
Since 29 is not divisible by any of these numbers, 29 is a prime number.
A game requires a player to choose a prime number as a code. The number should be the largest prime number under 31. Which prime number should the player choose?
The player should choose 29, the largest prime number under 31.
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 31 are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Therefore, the largest prime number under 31 is 29.
A teacher challenges her students: Find the prime numbers that are closest to 20 but less than 20.
19 is the prime number which is closest to 20.
19 is a prime number because it is only divisible by 1 and the number itself. The next prime number after 19 is 23, which is greater than 20. Therefore, the prime number closest to 20 and less than 20 is 19.
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.