How to Use the Prime Factorization Calculator

Select the type of calculation you need, enter your number(s), and click Calculate. The calculator provides four different modes for various prime number operations.

Calculator Modes

Prime Factorization

Breaks down any positive integer into its prime factors. For example, 360 = 2^3 × 3^2 × 5. The result shows each prime factor with its exponent (how many times it divides the number).

Prime Number Check

Determines whether a number is prime. A prime number is only divisible by 1 and itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23...

All Divisors

Finds every number that divides evenly into the given number. Also calculates the count and sum of all divisors. For example, divisors of 12 are: 1, 2, 3, 4, 6, 12.

Primes in Range

Lists all prime numbers between two values. Useful for finding primes in a specific range, like all primes between 1 and 100.

What Are Prime Numbers?

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. The first few primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47...

Why Prime Factorization Matters

Finding GCD (Greatest Common Divisor) and LCM (Least Common Multiple)
Simplifying fractions to lowest terms
Cryptography and computer security (RSA encryption)
Understanding number properties and relationships
Solving divisibility problems

Fundamental Theorem of Arithmetic

Every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors. This is why prime factorization is called the "DNA" of a number.