How to Check If a Number Is Prime and Find Its Prime Factors

A prime number has exactly two divisors: 1 and itself. Primes are the building blocks of all whole numbers and keep our online payments secure.

Quick answer

Enter a whole number up to one trillion. The tool says whether it is prime, shows its prime factorisation if it is not, and gives the nearest primes before and after.

Examples

• 29 is prime.
• 91 is not prime: 7 × 13.
• 360 = 2³ × 3² × 5.
• The primes either side of 100 are 97 and 101.

How to test by hand

To check whether n is prime, try dividing by primes up to √n. If none divide evenly, n is prime. For 97, √97 ≈ 9.8, so test 2, 3, 5 and 7; none divide, so 97 is prime.

Shortcuts

• Even numbers (except 2) are not prime.
• A number whose digit sum is divisible by 3 is divisible by 3.
• Numbers ending in 0 or 5 are divisible by 5.

Steps

1. Enter the number.
2. Read the result and factors.
3. Use the neighbouring primes for puzzles or code exercises.

Why primes matter

• Cryptography (RSA) relies on the difficulty of factoring a product of two large primes.
• Hash tables and random generators use primes.
• Maths puzzles and contests love them.

Note that 1 is not a prime number.