Prime Number Tools
Check prime numbers, find factors, and calculate GCD/LCM
Prime Number Properties
Prime Numbers
A prime number has exactly two factors: 1 and itself
First few primes: 2, 3, 5, 7, 11, 13, 17, 19, ...
Prime Factorization
Every number can be written as a product of prime numbers
Example: 12 = 2² × 3
GCD (Greatest Common Divisor)
Largest number that divides two numbers
Example: GCD(12,18) = 6
LCM (Least Common Multiple)
Smallest number that is divisible by two numbers
Example: LCM(4,6) = 12
Benefits & Features
Our prime number tools offer multiple advantages:
Comprehensive Tools
- Prime Number Checker
- Prime Factorization
- Prime Number Generator
- GCD & LCM Calculator
- Step-by-step Solutions
Educational Features
- Clear Explanations
- Visual Representations
- Number Properties
- Practice Problems
- Learning Resources
User-Friendly Interface
- Easy Tool Selection
- Clear Input Fields
- Instant Results
- Mobile-friendly Design
- Multiple Calculations
Frequently Asked Questions
A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself. For example, 2, 3, 5, 7, and 11 are prime numbers. The number 1 is not considered prime by definition.
To find prime factors, divide the number by the smallest possible prime number repeatedly until you can't divide anymore, then move to the next prime number. For example, to find prime factors of 12: 12 ÷ 2 = 6, 6 ÷ 2 = 3, 3 is prime. So 12 = 2 × 2 × 3 = 2² × 3.
For any two positive integers a and b, their GCD (Greatest Common Divisor) and LCM (Least Common Multiple) are related by the formula: GCD(a,b) × LCM(a,b) = a × b. This means if you know the GCD, you can easily find the LCM and vice versa.
There are infinitely many prime numbers. This was proven by Euclid around 300 BCE. His proof shows that if you have any finite list of prime numbers, you can always find another prime number not in your list.