Prime Factorization Calculator
Enter any integer to find its prime factors. This tool breaks down the number step-by-step and shows the result in exponential notation.
Result
Prime Factors of :
Exponential Notation:
Step-by-Step Division Method
We divide by the smallest prime numbers possible until we reach 1.
What is Prime Factorization?
Prime Factorization is the process of finding which prime numbers multiply together to make the original number.
For example, the prime factors of 12 are:
In exponential form, this is written as 22 × 3.
How to Find Prime Factors
The most common method is "Division by Primes":
- Start by dividing the number by the smallest prime number (2).
- If it divides evenly, write down 2 and divide the number.
- If it doesn't divide evenly, try the next prime number (3, then 5, then 7, etc.).
- Repeat the process with the new quotient until the only number left is 1.
Frequently Asked Questions
What is a Prime Number?
A prime number is a whole number greater than 1 whose only factors are 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23.
Why isn't 1 a prime number?
By definition, a prime number must have exactly two distinct positive divisors: 1 and itself. The number 1 only has one divisor (1), so it is not prime.
Is every number a product of primes?
Yes! The Fundamental Theorem of Arithmetic states that every integer greater than 1 is either a prime number itself or can be represented as the product of prime numbers in a unique way.
Can you find the prime factorization of a negative number?
Strictly speaking, prime factorization is defined for positive integers greater than 1. However, for a negative integer like -12, you can factor out -1 first (-1 × 12) and then find the prime factorization of the positive part (12 = 2 × 2 × 3). The result would be -1 × 2 × 2 × 3. Note that -1 is not a prime number.