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103 LearnersLast updated on August 29, 2025
Prime Numbers 1 to 150
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 150.
Prime Numbers 1 to 150
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 1 to 150 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 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.
List of All Prime Numbers 1 to 150
The list of all prime numbers from 1 to 150 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 150 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.
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 part of the set of odd numbers.
How to Identify Prime Numbers 1 to 150
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 find whether a number is prime or not:
By Divisibility Method:
To find whether a number is prime or not, use the divisibility method to check. If a number is divisible by 2, 3, or 5, it will result in a non-prime number. Prime numbers are only divisible by 1 and themselves. 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 a composite number into the product of its prime factors.
Rules for Identifying Prime Numbers 1 to 150
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 number is divisible by small prime numbers such as 2, 3, 5, and 7. If it's divisible by any of these numbers, it's not a prime number.
Rule 2: Prime Factorization:
In this method, we break down 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. First, list all numbers from 1 to 150. 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 150, approximately 12.25. The remaining unmarked numbers are the prime numbers.
Tips and Tricks for Prime Numbers 1 to 150
Use common shortcuts to memorize the prime numbers. For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
Practice using the method of Sieve of Eratosthenes efficiently.
Numbers like 4, 8, 9, 16, 25, and 36 are never prime.
Knowing the common powers of numbers helps in avoiding unnecessary checks.
Common Mistakes and How to Avoid Them in Prime Numbers 1 to 150
While working with prime numbers from 1 to 150, children might encounter some errors or difficulties. Here are some solutions to resolve those problems:
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 of 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 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 to 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 150, you don't have to check numbers divisible by 2, 3, 5, or 7 because they are not prime.
Prime Numbers Examples
Problem 1
Is 149 a prime number?
Yes, 149 is a prime number.
Explanation
The square root of 149 is approximately √149 ≈ 12.21.
We check divisibility by primes less than 12.21 (2, 3, 5, 7, 11).
149 ÷ 2 = 74.5
149 ÷ 3 = 49.666...
149 ÷ 5 = 29.8
149 ÷ 7 = 21.2857...
149 ÷ 11 = 13.5454...
Since 149 is not divisible by any of these numbers, 149 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 150. Which prime number will open the lock?
149 is the 3-digit code of the digital locker and the largest prime number under 150.
Explanation
Prime numbers are natural numbers that are greater than 1 and have no divisors other than 1 and the number itself.
The largest prime number under 150 is 149.
Therefore, the code to open the digital locker is 149.
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 closest to 60.
Explanation
59 is a prime number because it is only divisible by 1 and the number itself.
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.
FAQs on Prime Numbers 1 to 150
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 between 1 and 150?
Important Glossaries for Prime Numbers 1 to 150
- Prime numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves. For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and so on.
- Odd numbers: Numbers that are 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.
- Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a certain limit by iteratively marking the multiples of each prime number starting from 2.
- Divisibility test: A method to determine whether a number is prime by testing its divisibility by smaller prime numbers.
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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.
