Prime Number Checker
Check if a number is prime and find factors.
About Prime Number Checker
A prime number is only divisible by 1 and itself. The fundamental theorem of arithmetic states every integer > 1 has a unique prime factorization.
$$n \text{ is prime if divisible only by 1 and } n$$
How to use this calculator
- Enter a whole number greater than 1 into the checker.
- Click the button to test whether the number is prime.
- Read the result to see if the number is prime or composite.
- If it is not prime, use the factor list to see which numbers divide it evenly.
The formula explained
A number \(n\) is prime if its only divisors are 1 and \(n\) itself. If it has any other factor, then it is composite.
- n = the whole number being tested
- divisors = numbers that divide \(n\) evenly with no remainder
Step by step method
- Start with a whole number greater than 1.
- Check whether any number besides 1 and the number itself divides it evenly.
- If no other divisors work, the number is prime, otherwise it is composite.
Worked example
Problem. Check whether 29 is prime and list its factors.
- Test divisibility by whole numbers smaller than 29, such as 2, 3, 4, and 5.
- None of these numbers divide 29 evenly, so the only factors are 1 and 29.
- Because 29 has exactly two factors, it is prime.
Answer. 29 is prime, and its factors are 1 and 29.
Tips and common mistakes
- A number is never prime if it is divisible by 2, 3, 5, or any other whole number besides 1 and itself.
- Remember that 1 is not prime because it has only one factor, not two.
Frequently asked questions
How do I use the prime number checker?+
Enter a whole number, then the tool tells you whether it is prime and lists its factors. If the number is not prime, it will show the divisors that make it composite.
What does it mean when a number is prime?+
A prime number has exactly two positive factors, 1 and itself. For example, 13 is prime because only 1 and 13 divide it evenly.
Can the checker handle 1, 0, or negative numbers?+
No, 0 and 1 are not prime, and prime numbers are defined for positive integers greater than 1. Negative numbers are not considered prime in standard arithmetic.
What do the factors shown by the tool mean?+
The factors are the numbers that divide the input evenly with no remainder. If a number has more than two factors, it is composite, not prime.
How is a prime number different from a composite number?+
A prime number has exactly two factors, while a composite number has more than two. For example, 15 is composite because it can be divided by 1, 3, 5, and 15.
More Mathematics Tools
Explore related calculators in this category
You Might Also Like
Popular tools from other categories
Avogadro's Number Calculator
Convert between moles and number of particles. Free calculator with instant calculations, the underlying formula, and an easy-to-follow example.
CDN & Cache Header Guide
Understand which CDN serves a site from its response headers.
CORS Header Builder
Build the right CORS response headers for your API by choosing allowed origins, methods and headers.
Color Contrast Checker (WCAG)
Check the WCAG contrast ratio between a text and background color.
Can't Find the Right Calculator?
Try our AI Math Solver, type any problem in plain English and get instant step-by-step solutions.