Prime Factor Calculator
Calculate the prime factorization of any positive integer. Useful for mathematics, cryptography, and understanding number properties.
Enter a Number
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How to Use
Enter a number
Type any positive integer in the input field. The calculator supports numbers up to 10^15.
Calculate prime factors
Click the "Calculate Prime Factors" button to see the prime factorization of your number.
Analyze the results
View the prime factorization, factor tree, and additional information about your number.
What Are Prime Factors?
Prime factors are the prime numbers that, when multiplied together, give the original number. A prime number is a number greater than 1 that is only divisible by 1 and itself.
The prime factorization of 60 is 2² × 3 × 5.
This means that 60 = 2 × 2 × 3 × 5 = 4 × 15 = 60.
Every positive integer greater than 1 has a unique prime factorization. This is known as the Fundamental Theorem of Arithmetic.
Prime factorization is fundamental in number theory and has applications in:
- Cryptography and data security
- Finding greatest common divisors (GCD)
- Finding least common multiples (LCM)
- Simplifying fractions
- Solving various mathematical problems
Frequently Asked Questions
Prime factorization is the process of breaking down a number into a product of prime numbers. For example, the prime factorization of 12 is 2² × 3, which means 12 = 2 × 2 × 3.
To find the prime factorization of a number, you divide it by the smallest possible prime number (usually starting with 2), and continue dividing the quotient by the smallest possible prime until you reach 1. The prime numbers used in these divisions are the prime factors.
A perfect number is a positive integer that is equal to the sum of its proper divisors (all divisors excluding the number itself). For example, 6 is a perfect number because its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6.
Factoring very large numbers can be computationally demanding. For numbers with more than 15 digits, the calculation may take too long or exceed browser capabilities. The difficulty of factoring large numbers is actually the basis for some encryption algorithms used in cybersecurity.