Prime Factorization Calculator
Find the prime factorization of any number. See prime factors in exponential form, factor trees, and all divisors.
n = p₁^a₁ × p₂^a₂ × ... × pₖ^aₖPrime Factorization
Factorization
2^3 × 3^2 × 5
Enter a Number
Enter a positive integer up to 999,999,999
Step-by-Step Division
360 = 2^3 × 3^2 × 5
Prime Factor Breakdown
| Prime Factor | Count | Contribution |
|---|---|---|
| 2 | 3 | 2^3 = 8 |
| 3 | 2 | 3^2 = 9 |
| 5 | 1 | 5 |
All Divisors (24)
Factor Pairs
All Divisors List
Number Properties
Is Prime?
No
Is Even?
Yes
Perfect Square?
No
Perfect Cube?
No
First 25 Prime Numbers
Highlighted primes appear in the factorization of 360
Prime Factorization
Factorization
2^3 × 3^2 × 5
?How to Find Prime Factorization
Prime factorization breaks a number into a product of prime numbers. To find prime factors, divide by the smallest prime (2) repeatedly, then try 3, 5, 7, and so on until the quotient is 1. For example, 60 = 2 x 2 x 3 x 5 = 2^2 x 3 x 5. Every integer greater than 1 has a unique prime factorization.
What is Prime Factorization?
Prime factorization is the process of expressing a composite number as a product of its prime factors. According to the Fundamental Theorem of Arithmetic, every integer greater than 1 can be represented uniquely as a product of prime numbers. Prime factorization is essential for finding GCF, LCM, simplifying fractions, and cryptography.
Key Facts About Prime Factorization
- Prime factorization expresses a number as a product of prime numbers
- Every integer > 1 has a unique prime factorization (Fundamental Theorem of Arithmetic)
- Prime numbers are only divisible by 1 and themselves: 2, 3, 5, 7, 11, 13...
- 2 is the only even prime number
- Exponential form groups repeated primes: 2 x 2 x 2 x 3 = 2^3 x 3
- Prime factorization is used to find GCF and LCM
- A number is a perfect square if all prime factors have even exponents
- The number of divisors = product of (exponent + 1) for each prime factor
Quick Answer
Prime factorization breaks a number into a product of prime numbers. To find prime factors, divide by the smallest prime (2) repeatedly, then try 3, 5, 7, and so on until the quotient is 1. For example, 60 = 2 x 2 x 3 x 5 = 2^2 x 3 x 5. Every integer greater than 1 has a unique prime factorization.
Frequently Asked Questions
Prime factorization breaks down a number into a product of prime numbers. Every integer greater than 1 can be uniquely expressed as a product of primes. For example, 60 = 2² × 3 × 5. This is called the Fundamental Theorem of Arithmetic.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29... Note that 2 is the only even prime number.
Start dividing by the smallest prime (2) until it no longer divides evenly. Then try the next prime (3), and continue. Keep going until the quotient is 1. The divisors used are the prime factors.
Exponential form groups repeated prime factors using exponents. Instead of 2 × 2 × 2 × 3 × 3, write 2³ × 3². This is more compact and clearly shows how many times each prime appears.
Prime factorization is used to find GCD and LCM, simplify fractions, determine if a number is a perfect square, solve problems in cryptography (RSA encryption relies on it), and understand number properties.
Last updated: 2025-01-15
Prime Factorization
Factorization
2^3 × 3^2 × 5