Prime Number Checker
Verify if a number is prime or composite. Instantly calculate its prime factorization and view a complete list of all its mathematical factors.
17 is a PRIME number
All Factors (2)
1, 17
Prime Factorization
17
Prime vs. Composite Numbers
In mathematics, every whole number greater than 1 falls into one of two categories: prime or composite. Our Prime Number Checker is designed to instantly analyze any number and categorize it, while showing you exactly how the math works behind the scenes.
Prime Numbers
A prime number can only be divided cleanly (without a remainder) by 1 and itself. The smallest prime numbers are 2, 3, 5, 7, 11, and 13. Prime numbers are the foundational building blocks of mathematics and modern computer encryption systems.
Composite Numbers
A composite number has more than two factors. For example, 4 is a composite number because it can be divided by 1, 2, and 4.
What is Prime Factorization?
The Fundamental Theorem of Arithmetic states that every integer greater than 1 is either a prime itself or can be represented as a unique product of prime numbers. This is known as Prime Factorization.
For example, the number 12 is composite. Its prime factorization is 2 × 2 × 3. Our calculator automatically computes this for any valid input, breaking down massive numbers into their most basic prime components in milliseconds.
Frequently Asked Questions About Prime Numbers
What is a prime number?
A prime number is a whole number greater than 1 whose only divisors are 1 and itself. Examples include 2, 3, 5, 7, 11, and 13.
Is 1 a prime number?
No, the number 1 is neither prime nor composite. By definition, a prime number must have exactly two distinct positive divisors: 1 and the number itself.
What is prime factorization?
Prime factorization is finding which prime numbers multiply together to make the original number. For example, the prime factorization of 12 is 2 × 2 × 3.
Does this show prime factorization?
Yes. Instantly check if a number is prime and get its complete prime factorization.