Prime Factorization
Factorize integers into prime factors, displaying exponential and expanded forms, primality check, and complete divisor list. Supports up to 18 digits
Features
Both exponential and expanded forms
Display 360 as both 2³ × 3² × 5 and in full multiplication format
Factorize up to 18-digit integers
Identify large numbers that exceed calculator limits and determine if they are prime
View divisor count and complete list
See the number of divisors and a sorted list, collapsible for easy viewing
Copy formulas and lists with one click
Transfer results directly to your notebook or chat exactly as displayed
How to Use
Enter the integer to factorize
Input a single integer (2 or more, up to 18 digits) in the input field. Full-width digits and comma-separated numbers are also accepted
Press "Factorize"
Click the button or press Enter in the input field to start the calculation
Review the formula and primality
Check the exponential form, expanded form, and divisor count
Open the divisor list and copy
Expand the divisor list and use the copy buttons to save results
Use Cases
Homework and test study verification
Check if your prime factorization answers are correct
Preparation for square roots and fraction reduction
Simplify expressions under radicals and find common factors before reducing fractions
Verify if large numbers are prime
Check if 17- to 18-digit integers are prime and discover their prime factors
Programming and puzzle verification
Compare number properties like divisor count with your custom code output
Basic Knowledge
What is prime factorization?
Prime factorization is expressing an integer of 2 or more as a product of prime numbers only. For example, 360 can be written as 2³ × 3² × 5, and except for the order of multiplication, every integer has exactly one unique factorization.
How to perform prime factorization
Prime factorization is found by repeatedly dividing by the smallest primes in order, continuing until the quotient becomes 1. The final answer is the product of all the primes you divided by.
- First, divide by 2 as much as possible：Test if the number is divisible by 2, and if it is, keep dividing the quotient by 2 until it is no longer divisible
- Move to the next prime：When no longer divisible by 2, move to 3, 5, 7, 11, and so on, dividing by each prime the same way until no longer divisible
- Example with 360：360 divided by 2 three times gives 45, 45 divided by 3 twice gives 5, and 5 divided by 5 gives 1, so 360 = 2³ × 3² × 5
How to find the number of divisors
The number of divisors is found by adding 1 to each exponent in the prime factorization and multiplying all these results together. For 360 = 2³ × 3² × 5, the calculation is (3+1) × (2+1) × (1+1) = 24, so 360 has 24 divisors
Safety and Privacy
Runs entirely in your browser
Your input data is processed only within your browser and is never sent externally.
Processing only in your browser
Prime factorization calculation is processed entirely within your browser, and input data is not sent to any server.
Communications encrypted with HTTPS
Page loading is also encrypted by TLS, and content cannot be read by third parties.
No transmission to third parties
Input content is not sent to external services such as ad networks or trackers.
No automatic saving of results
Numbers you input and input suggestions are not stored on the server.
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Updates
- update #399
Prime factorization added. Display integers up to 18 digits as exponential expressions and divisor lists
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