Prime Factors Calculator
Find the prime factorization of any number. Break down numbers into prime factors.
Find prime factors of any positive integer. Shows prime factorization, exponential form, all factors, and a visual factor tree.
Quick examples:
How to Use
- Enter any whole number greater than 1
- Click "Find Prime Factors" to calculate
- View the complete prime factorization with division steps
- See the exponential form and unique prime factors
What is Prime Factors Calculator?
Prime factorization is the process of breaking down a number into its prime number components. A prime number is a number greater than 1 that can only be divided evenly by 1 and itself. Every composite number can be expressed as a unique product of prime numbers, known as its prime factorization.
Formula
Method:
1. Start with the smallest prime (2)
2. Divide the number by this prime while possible
3. Move to the next prime and repeat
4. Continue until the quotient is 1
Example: 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7
Examples
- 12 = 2² × 3 (2 × 2 × 3)
- 60 = 2² × 3 × 5 (2 × 2 × 3 × 5)
- 100 = 2² × 5² (2 × 2 × 5 × 5)
- 84 = 2² × 3 × 7 (2 × 2 × 3 × 7)
- 360 = 2³ × 3² × 5
FAQ
What is a prime number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
Why is prime factorization important?
Prime factorization is used to find GCD and LCM, simplify fractions, solve problems in cryptography, and understand number properties. It's fundamental in number theory.
Is the prime factorization unique?
Yes! The Fundamental Theorem of Arithmetic states that every integer greater than 1 has a unique prime factorization, regardless of the order of factors.