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Factor Calculator
Type a positive whole number and get all of its factors in order, the pairs that multiply to it, its prime factorization and whether it is prime.
Answer
Enter your numbers or pick an example — the answer and the steps appear here instantly.
Everything about one number
How to use the factor calculator
Enter one number
Any positive whole number up to 10¹² works, such as 360 or 1001. Clicking an example chip loads a sample number instead.
Calculate
The factors, pairs, factor count, prime factorization and prime verdict appear at once. Every value is an exact integer, so nothing here is rounded or marked ≈.
Copy or ask for an explanation
Copy what you need. With “Explain step by step”, the AI Math Solver describes the trial division in its own words; that is useful, though it may contain mistakes.
How to find all factors by hand
Use trial division, but only up to the square root. Divide the number by 1, 2, 3 and so on; each divisor that leaves no remainder gives you two factors at once. For 360, √360 ≈ 18.97, so you only test 1 through 18. The hits are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15 and 18, and their partners are 360, 180, 120, 90, 72, 60, 45, 40, 36, 30, 24 and 20.
Stopping at the square root works because factors come in pairs, one at or below the root and one at or above it. A perfect square has one pair with equal partners, 36 = 6 × 6, which is why 36 has an odd number of factors: 1, 2, 3, 4, 6, 9, 12, 18 and 36.
The prime factorization predicts the factor count. Add 1 to each exponent and multiply: 360 = 2³ × 3² × 5 has (3 + 1)(2 + 1)(1 + 1) = 24 factors, because every factor picks one of 2⁰ to 2³, one of 3⁰ to 3², and either 5⁰ or 5¹.
A number greater than 1 is prime when trial division up to its square root finds nothing. For 97, √97 ≈ 9.85, and 97 is not divisible by 2, 3, 5 or 7, so 97 is prime. The number 1 is neither prime nor composite.
Frequently asked questions
Numbers up to 10¹², or one trillion, are accepted. Trial division only has to reach the square root, which is at most one million, so the work stays manageable for your browser.
Factors are all the whole numbers that divide a number evenly; prime factors are the primes among them. 12 has six factors (1, 2, 3, 4, 6, 12) but only two prime factors, 2 and 3, and its prime factorization is 2² × 3.
No. A prime has exactly two factors, 1 and itself, and 1 has only one. By the same rule, 2 is the only even prime.
They are what you look for when factoring a quadratic or finding the sides of a rectangle with a given area. To factor x² + 7x + 12, you need the pair of 12 that adds to 7, which is 3 and 4.
Yes. It runs entirely in your browser, needs no account and sends nothing to a server. The AI explanation is separate: free within the Pro plans* (*fair use: up to 300 runs a day, counted together for the writing, study and code tools), 2 credits for accounts with no plan, plus a free opening preview for signed-out visitors.
Use it to check the factors you found and to spot the ones you missed. When the worksheet is graded, the rules your teacher sets for calculators and AI help apply.
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Factor any number up to a trillion
See every factor, each pair and the prime factorization in one result.
Find factors- Sorted factor list
- Prime check included
- Trial division to √n