How do I tell if a number is prime?

If this calculator returns the same number you entered, that number is prime — it has no factors other than 1 and itself. Examples: 17, 97, 101 are prime.

What is prime factorisation?

Prime factorisation expresses a number as a product of prime numbers. For 84: 84 = 2² × 3 × 7. Every integer greater than 1 has a unique prime factorisation (Fundamental Theorem of Arithmetic).

Why are prime factors important?

Prime factors are foundational in mathematics and cryptography. RSA encryption — used to secure internet traffic — relies on the difficulty of factorising very large numbers into primes.

Prime Factor Calculator — Smallest Prime Factor

The Prime Factor Calculator finds the smallest prime factor of any positive integer. A prime factor is a prime number that divides the input exactly. If the smallest prime factor equals the number itself, the number is prime. This is a fundamental tool in number theory, cryptography, and mathematics education.

Number

How to Use This Calculator

1
Enter any positive integer greater than 1.
2
Click Calculate to find the smallest prime factor.
3
If the result equals your input number, the number is prime.

Frequently Asked Questions

A prime factor is a factor of a number that is itself a prime. For example, the prime factors of 84 are 2, 2, 3, and 7 (since 84 = 2 × 2 × 3 × 7).

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