Prime Divisor Calculator
Prime Divisors works out Prime factorization and Written out in full from Number and List every divisor. The default figures on this page give prime factorization of 2^3 x 3^2 x 5; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
9 steps
- 360 / 2 = 180
- 180 / 2 = 90
- 90 / 2 = 45
- 45 / 3 = 15
- 15 / 3 = 5
- 5 / 5 = 1
- Nothing left to divide, so 360 = 2^3 x 3^2 x 5.
- Number of divisors = product of (exponent + 1) = (3+1) x (2+1) x (1+1) = 24.
- Sum of divisors = product of (p^(e+1)-1)/(p-1) = 1170; subtracting 360 leaves 810 for the proper divisors.
Distinct prime factorstable
Exponent of each primetable
Its 7 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the Prime Divisors calculates
Breaks a whole number into its prime factors, tests whether it is prime, and reports the divisor count, divisor sum, all divisors and Euler totient.
How to use this Prime Divisors
Enter Number and List every divisor. Prime factorization updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Prime factorization, Written out in full and Distinct prime factors.
The method follows NIST Digital Library of Mathematical Functions, §27.2-27.3 (fundamental theorem of arithmetic; divisor and totient functions), J. M. Pollard, "A Monte Carlo method for factorization", BIT 15 (1975) 331-334; R. P. Brent, "An improved Monte Carlo factorization algorithm", BIT 20 (1980) 176-184 and J. Sorenson and J. Webster, "Strong pseudoprimes to twelve prime bases", Mathematics of Computation 86 (2017) - the 12-base Miller-Rabin test is deterministic below 3.317e24.
What you can compare
Change one input at a time to see how it affects Prime factorization, Written out in full and Distinct prime factors. The inputs you can vary are Number and List every divisor.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
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Frequently asked questions
What are the prime divisors of 100?
On the figures this page opens with, the prime factorization is 2³ x 3² x 5. No single number fits everyone: it follows Number and List every divisor, so enter your own above and the answer updates as you type.
What are the prime divisors of 12?
It needs Number and List every divisor. Nothing else is required, and the figures stay in your browser.
How many divisors do prime numbers have?
The result gives Prime factorization, Written out in full, Distinct prime factors, Exponent of each prime, Number of distinct primes and Prime factors counted with multiplicity, each labelled with its unit so the figure can be read on its own.
What information do I need for the Prime Divisors?
You need Number and List every divisor. The page opens with default figures that give prime factorization of 2^3 x 3^2 x 5, so you can see the scale before entering your own.
What does this Prime Divisors show?
It shows Prime factorization, Written out in full, Distinct prime factors, Exponent of each prime, Number of distinct primes, Prime factors counted with multiplicity, Is prime and Smallest prime factor, with the working and any warnings for your entries.
Can I check how the Prime Divisors result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.