Prime Factorization Calculator
Free prime factorization calculator. Shows results like 2^3 × 3^2 × 5 with division steps and a prime-number check.
How to use
- Enter an integer (2 or greater).
- Press “Factorize”.
- See the prime product, division steps, and whether it is prime.
Examples
- 36 = 2^2 × 3^2
- 84 = 2^2 × 3 × 7
- 97 is a prime number
When to use it (grade level)
Prime factorization is taught in the first year of middle school. It deepens your grasp of factors and multiples and connects to greatest common divisors, least common multiples, and simplifying fractions. This tool suits lesson preview and review, checking home study, and confirming your work before a test.
Prime factorization means breaking an integer into a product of prime numbers only. For example, 36 = 2 × 2 × 3 × 3.
Primes and composite numbers
A prime number is a whole number greater than 1 that can be divided evenly only by 1 and itself: 2, 3, 5, 7, 11, 13, 17, 19, and so on. A number that can be written as a product of two or more primes (such as 4, 6, 8, or 9) is called a composite number.
Note that 1 is neither prime nor composite. A prime is defined as having exactly two divisors — 1 and itself — and 1 has only one divisor.
The division steps and exponents
The basic method is to divide by the smallest primes in order. For 36: divide by 2 to get 18, by 2 again to get 9; since 9 is not divisible by 2, move to the next prime 3 to get 3, then by 3 again to get 1. The primes we used are 2 × 2 × 3 × 3.
Group repeated primes using exponents, a small raised number showing how many times each appears. With two 2s and two 3s, we write 36 = 2^2 × 3^2. Exponents keep even large numbers tidy.
Common mistakes
Three slip-ups are common. First, treating 1 as a prime — it is not included. Second, dividing by a non-prime such as 4 or 6 partway through; always divide by primes only. Third, stopping too early on a large number when it can still be divided. Keep dividing until the quotient reaches 1.
Using it for GCD and simplifying
Once you can factorize, gather the shared primes of two numbers to get the greatest common divisor, and collect all primes to their highest needed powers to get the least common multiple. For example, 12 = 2^2 × 3 and 18 = 2 × 3^2, so the shared part 2 × 3 = 6 is the greatest common divisor.
It also helps with simplifying fractions: factorize the numerator and denominator, and the common primes show exactly what to cancel. Try it alongside the GCD and LCM calculator and the fraction calculator.
FAQ
Is 1 a prime number?
No. A prime number is greater than 1 and has only two positive divisors.
Can I use very large numbers?
The first version supports up to 9,999,999,999.
What do the steps show?
They show each division by a prime factor, in order.