Prime Factorization Calculator
Break any integer into its prime factors with exponents.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Request a ToolHow to Use the Prime Factorization Calculator
Enter any non-zero integer and its prime factorization appears instantly. The breakdown shows each prime factor and how many times it divides the number.
- Enter a number. Type any positive or negative integer (up to 1 trillion).
- Read the factorization. The result shows the number as a product of prime powers (e.g., 360 = 2^3 x 3^2 x 5).
- Check the breakdown. See individual factors, total count, and whether the number itself is prime.
About Prime Factorization
Every integer greater than 1 can be written as a unique product of prime numbers (the Fundamental Theorem of Arithmetic). For example, 360 = 2^3 x 3^2 x 5. This factorization is unique regardless of the order of the factors.
Prime factorization is used to find the GCF and LCM of numbers, simplify fractions, and solve problems in cryptography. This calculator uses trial division, testing each potential factor starting from 2 up to the square root of the number.
Frequently Asked Questions
What is prime factorization?
Prime factorization breaks a number into the product of prime numbers that multiply together to give the original. For example, 12 = 2 x 2 x 3 = 2^2 x 3.
Can you factor negative numbers?
Yes. The calculator factors the absolute value and prepends -1 as a factor. For example, -12 = -1 x 2^2 x 3.
What is the largest number this can factor?
This calculator handles numbers up to 1 trillion (1,000,000,000,000). For very large numbers with large prime factors, the trial division method may take longer.