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103 LearnersLast updated on August 29, 2025
Prime Numbers 1 to 120
The natural numbers greater than 1 that are not divisible by any other numbers except 1 and themselves are called prime numbers. Prime numbers have exactly two distinct positive divisors: 1 and the number itself. Beyond mathematics, prime numbers are crucial in fields like cryptography, computer algorithms, and more. In this topic, we will explore the prime numbers from 1 to 120.
Prime Numbers 1 to 120
A prime number is a natural number that cannot be divided evenly by any other number except 1 and itself. Here are some fundamental properties of prime numbers:
Every number greater than 1 is divisible by at least one prime number.
Any two distinct prime numbers are always relatively prime to each other.
Every even positive integer greater than 2 can be expressed as the sum of two prime numbers (Goldbach's conjecture, which remains unproven).
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 120 Chart
A prime number chart displays prime numbers in ascending order up to a specified limit, making it easier to identify prime numbers within a range.
A prime number chart helps in foundational mathematics and the fundamental theorem of arithmetic.
List of All Prime Numbers 1 to 120
The list of all prime numbers from 1 to 120 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 120 include:
Prime Numbers - Odd Numbers
Except for the number 2, all prime numbers are odd because they cannot be evenly divided by 2. Hence, aside from 2, all prime numbers are considered a subset of odd numbers.
How to Identify Prime Numbers 1 to 120
Prime numbers are natural numbers greater than 1 that are only divisible by 1 and themselves. Here are two methods to determine if a number is prime:
Divisibility Method:
To determine if a number is prime, check its divisibility. If a number is divisible by any prime number up to its square root, it is not prime. For example: To check if 47 is a prime number,
47 ÷ 2 = 23.5 (remainder ≠ 0)
47 ÷ 3 = 15.67 (remainder ≠ 0)
47 ÷ 5 = 9.4 (remainder ≠ 0)
Since no divisors are found, 47 is a prime number.
Prime Factorization Method:
This method involves breaking down a composite number into its prime factors, demonstrating that it is not prime. This method helps identify prime numbers up to 120 by using the smallest prime building blocks.
Rules for Identifying Prime Numbers 1 to 120
Rule 1: Divisibility Check:
Prime numbers are natural numbers greater than 1 with no divisors other than 1 and the number itself. In this rule, we check divisibility by small prime numbers. If divisible, it is not prime.
Rule 2: Prime Factorization:
Break down numbers into their prime factors, showing them as products of prime numbers.
Rule 3: Sieve of Eratosthenes Method:
An ancient algorithm to find all prime numbers up to a limit. List numbers from 1 to 120, start with 2, and mark all multiples of 2 as non-prime. Repeat with the next unmarked number, continuing to numbers up to the square root of 120 (approximately 10.95). The unmarked numbers are prime.
Tips and Tricks for Prime Numbers 1 to 120
Memorize small prime numbers like 2, 3, 5, 7, 11, and 13 for quick reference.
Practice using the Sieve of Eratosthenes method effectively.
Understand that numbers like 4, 8, 9, 16, and 25 are not prime.
Recognizing common squares helps avoid unnecessary checks.
Common Mistakes and How to Avoid Them in Prime Numbers 1 to 120
When working with prime numbers 1 to 120, students may encounter errors. Here are some solutions:
Mistake 1
Confusing composite numbers with prime numbers.
A prime number has exactly two divisors: 1 and itself. Remember that composite numbers have more than two divisors.
For example, 9 is not a prime number because it has more than two divisors.
Mistake 2
Including 1 as a prime number.
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 Sieve of Eratosthenes efficiently or check divisibility by primes up to the square root of the number.
For example, when checking 77, stop once you reach √77.
Mistake 4
Not realizing about the primes in the larger prime range.
Consistently practice identifying larger primes to enhance skills. The Sieve of Eratosthenes method is helpful for this.
Mistake 5
Forgetting that multiples of any prime number are not prime.
Mark all multiples of known prime numbers as non-prime. For instance, when checking numbers up to 120, avoid numbers divisible by 2, 3, 5, or 7 as they are not prime.
Prime Numbers Examples
Problem 1
Is 113 a prime number?
Yes, 113 is a prime number.
Explanation
The square root of 113 is approximately 10.63.
Check divisibility by primes less than 10.63
(2, 3, 5, 7).
113 ÷ 2 = 56.5
113 ÷ 3 = 37.67
113 ÷ 5 = 22.6
113 ÷ 7 = 16.14
Since 113 is not divisible by any of these numbers, it is a prime number.
Problem 2
Sophie wants to set a lock with a 3-digit code. The code is the largest prime number under 120. What number will she use?
113 is the 3-digit code for the lock and the largest prime number under 120.
Explanation
Prime numbers are natural numbers greater than 1 with no divisors other than 1 and the number itself.
The prime numbers under 120 include 2, 3, 5, 7, 11, 13, and so on.
113 is the largest prime number under 120, so the code for the lock is 113.
Problem 3
A teacher asks students to find the prime numbers closest to 50 but less than 50.
47 is the prime number closest to 50.
Explanation
47 is a prime number because it is only divisible by 1 and itself.
The next prime number after 47 is 53, which is greater than 50.
Thus, the prime number closest to and less than 50 is 47.
FAQs on Prime Numbers 1 to 120
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 1 to 120?
Important Glossaries for Prime Numbers 1 to 120
- 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, and 29.
- Odd numbers: Numbers not divisible by 2. All prime numbers except 2 are odd. For example, 3, 5, 7, 9, and 11.
- Composite numbers: Numbers with more than two factors. For example, 12 is a composite number, divisible by 1, 2, 3, 4, 6, and 12.
- Sieve of Eratosthenes: An algorithm to find all prime numbers up to a specified limit by marking multiples of primes.
- Divisibility: A method to determine if a number can be evenly divided by another. Used to test whether a number is prime.
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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.
