What This Calculator Does

This prime calculator combines three related tasks that are often confused: checking whether an integer is prime, factoring an integer into prime factors, and listing every prime in a closed interval. Each mode has its own supporting output: prime check shows the smallest factor, neighboring primes, and factorization; factor mode shows exponents and the total number of positive divisors; range mode returns the complete list and count.

It is useful for classroom practice, introductory number theory, programming checks, factor analysis before fraction reduction, and moderate-size prime lookups. If you need to use prime factors for a greatest common factor or least common multiple, see the GCF calculator and LCM calculator. For fraction arithmetic, use the fraction calculator.

When to Use It

• You want to check whether 97 is prime or find a composite number's smallest prime factor.
• You want to write 84 as 2^2 × 3 × 7.
• You want the number of positive divisors implied by a prime factorization.
• You want every prime from 10 through 30.
• You want the previous and next prime around a selected integer.

Inputs Explained

Mode

The page provides three modes:

• Prime Check (check) tests an integer and shows its smallest factor, neighboring primes, and factorization.
• Factorization (factor) factors one integer and shows each prime exponent plus the positive divisor count.
• Prime Range (range) lists every prime from the start value through the end value, including both endpoints.

Single Number