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104 LearnersLast updated on August 30, 2025
Prime Numbers 100 to 120
Prime numbers are the natural numbers greater than 1 that can only be divided by 1 and themselves. They play an essential role not only in mathematics but also in fields such as cryptography and coding theory. In this topic, we will focus on the prime numbers between 100 and 120.
Prime Numbers 100 to 120
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Prime numbers between 100 and 120 exhibit these properties:
They are only divisible by 1 and the number itself.
They are often used in encryption and security algorithms.
Except for 2, all prime numbers are odd.
Prime numbers are fundamental in number theory.
Prime Numbers 100 to 120 Chart
A prime number chart is a visual tool that displays prime numbers in a specified range.
This chart helps in quickly identifying prime numbers within the range of 100 to 120. Such charts are useful for educational purposes and practical applications in various fields of mathematics.
List of All Prime Numbers 100 to 120
The list of prime numbers between 100 and 120 includes: - 101 - 103 - 107 - 109 - 113
These numbers are only divisible by 1 and themselves.
Prime Numbers - Odd Numbers
While 2 is the only even prime number, all prime numbers between 100 and 120 are odd.
This characteristic helps in distinguishing prime numbers from other numbers within this range.
How to Identify Prime Numbers 100 to 120
There are two main methods to determine if numbers between 100 and 120 are prime:
Divisibility Method:
Check divisibility by smaller prime numbers (e.g., 2, 3, 5, 7). If a number is not divisible by any of these, it is prime. Example: To determine if 107 is prime:
107 ÷ 2 = 53.5 (not divisible)
107 ÷ 3 ≈ 35.67 (not divisible)
107 ÷ 5 = 21.4 (not divisible)
107 ÷ 7 ≈ 15.29 (not divisible)
Since 107 is not divisible by any of these, it is a prime number. 2.
Prime Factorization Method:
This involves expressing a number as a product of its prime factors. If a number cannot be decomposed into smaller prime factors, it is itself a prime number.
Rules for Identifying Prime Numbers 100 to 120
Rule 1: Divisibility Check:
Numbers greater than 1 with no divisors other than 1 and itself are prime. Check divisibility by 2, 3, 5, and 7 to determine primality.
Rule 2: Prime Factorization:
Decompose numbers into their prime factors. If a number cannot be broken down further, it is prime.
Rule 3: Sieve of Eratosthenes Method:
This ancient algorithm identifies all prime numbers up to a given limit. List numbers from 100 to 120, starting with the smallest prime, 101. Mark multiples of each prime found as non-prime. Unmarked numbers are primes.
Tips and Tricks for Prime Numbers 100 to 120
Memorize small prime numbers such as 101, 103, 107, 109, and 113.
Use the Sieve of Eratosthenes method for efficient identification.
Recognize that numbers like 104, 108, 110 are not primes since they are divisible by small primes.
Common Mistakes and How to Avoid Them in Prime Numbers 100 to 120
While learning about prime numbers between 100 and 120, some common errors may arise. Here are solutions to these issues:
Mistake 1
Confusing composite numbers with prime numbers.
Composite numbers have more than two divisors.
For example, 110 is not a prime number because it is divisible by 2, 5, and 11.
Mistake 2
Including 1 as a prime number.
Remember, prime numbers are greater than 1. The number 1 is not prime as it only has one divisor.
Mistake 3
Not efficiently using the prime checking method.
Use the Sieve of Eratosthenes or check divisibility by small primes efficiently.
For example, when checking 113, stop once you reach its approximate square root.
Mistake 4
Overlooking prime numbers in a specific range.
Practice identifying primes in the range 100 to 120 to enhance your skills. The Sieve of Eratosthenes method is helpful for this.
Mistake 5
Forgetting that multiples of any prime number are not prime.
Eliminate multiples of small primes quickly.
For example, numbers divisible by 2, 3, or 5 in this range are not prime.
Prime Numbers Examples
Problem 1
Is 109 a prime number?
Yes, 109 is a prime number.
Explanation
The square root of 109 is approximately 10.44.
Check divisibility by primes less than 10.44 (2, 3, 5, 7):
109 ÷ 2 = 54.5
109 ÷ 3 ≈ 36.33
109 ÷ 5 = 21.8
109 ÷ 7 ≈ 15.57
Since 109 is not divisible by any of these numbers, it is a prime number.
Problem 2
Tom is trying to find a safe combination with a number between 100 and 120. He wants the largest prime number less than 120. Which number should he choose?
Tom should choose 113, the largest prime number less than 120.
Explanation
Prime numbers are natural numbers greater than 1 and have no divisors other than 1 and themselves.
The prime numbers between 100 and 120 include 101, 103, 107, 109, and 113.
Among these, 113 is the largest prime number under 120.
Problem 3
A teacher asks her students: Find the prime numbers closest to 110 but less than 110.
109 is the prime number closest to 110.
Explanation
109 is a prime number because it is only divisible by 1 and itself.
The next prime number after 109 is 113, which is greater than 110.
Therefore, the prime number closest to 110 and less than 110 is 109.
FAQs on Prime Numbers 100 to 120
1.Give some examples of prime numbers.
2.Explain prime numbers in math.
3.Is 2 the smallest prime number?
4.Are there any prime numbers between 100 and 120?
5.How can you check if a number between 100 and 120 is prime?
Important Glossaries for Prime Numbers 100 to 120
- Prime numbers: Natural numbers greater than 1, divisible only by 1 and themselves. Examples: 101, 103, 107.
- Divisibility: A method to check if a number can be evenly divided by another number.
- Composite numbers: Numbers with more than two divisors. Example: 110 (divisible by 2, 5, 11).
- Sieve of Eratosthenes: An algorithm to find all prime numbers up to a specified number by marking multiples of primes.
- Factorization: The process of breaking down a number into its prime components.
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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.
