Prime Number Checker
Check if a number is prime, find prime factors, and analyze divisibility
Enter a positive integer (1 to 10,000,000)
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Theory & Formula
Prime Numbers
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Prime numbers are the building blocks of all natural numbers.
Prime Numbers
The first prime number is 2, which is also the only even prime. All other primes are odd numbers.
First primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37...
Composite Numbers
A composite number is a positive integer that has at least one divisor other than 1 and itself. In other words, it can be factored into smaller positive integers.
First composites: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20...
Fundamental Theorem of Arithmetic
Every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors.
Example
The number 60 can be factored as:
This means 60 = 2 × 2 × 3 × 5. No other combination of primes multiplies to 60.