Prime Factorization Calculator
Any whole number up to 1,000,000,000,000. The sign is ignored.
Enter a whole number to see its prime factorization and divisors.
- Distinct prime factors
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- Number of divisors
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What is Prime Factorization Calculator
This calculator breaks any whole number down into its prime factors. Enter a value and you get the factorization in exponent form (for example 360 = 2^3 × 3^2 × 5), the list of distinct primes, whether the number is prime or composite, the divisor count and every divisor in order. It works on the absolute value, so the sign of a negative number is ignored.
How to use
- Type a whole number into the field.
- Read the prime or composite badge at the top.
- Check the factorization written in exponent form.
- Scroll down for the full list of divisors and the divisor count.
When to use it
Reducing a fraction like 84/126 and want the shared factors fast? Enter 84 to see 2^2 × 3 × 7, then 126 to see 2 × 3^2 × 7, and cancel the common 2 × 3 × 7. The same breakdown helps with simplifying radicals, finding a common denominator, checking whether a number is prime for a maths class, or seeing the building blocks behind a cryptography exercise.
Frequently asked questions
What is prime factorization?
Prime factorization writes a number as a product of prime numbers. Every whole number above 1 has exactly one such factorization. For example, 360 = 2 × 2 × 2 × 3 × 3 × 5, written compactly as 2^3 × 3^2 × 5.
How do I know if a number is prime?
A prime number has exactly two divisors: 1 and itself. The tool checks this directly and shows a Prime badge when it applies. If the number has any other divisor it is composite, and the tool lists all of them.
Are 0 and 1 prime?
No. 1 is neither prime nor composite, and its only divisor is 1. 0 has no prime factorization and is divisible by every integer, so its divisor count is shown as infinite.
What is the largest number I can factor?
You can factor any whole number up to 1,000,000,000,000 (one trillion). The tool uses trial division up to the square root, which stays fast within that range.
Can I share this tool with my number pre-filled?
Yes. The URL updates automatically as you type. Copy it from the address bar or use the Share button, and anyone who opens the link will see your exact number ready to go.
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