Divisors[n]
gives a list of the integers that divide n.


Divisors
Divisors[n]
gives a list of the integers that divide n.
Details and Options

- Divisors[n,GaussianIntegers->True] includes divisors that are Gaussian integers.
Examples
open all close allScope (2)
For integer input, integer divisors are returned:
For Gaussian integer input, Gaussian divisors are produced:
Divisors threads element‐wise over list arguments:
Options (3)
Applications (3)
Find all perfect numbers less than 10000:
Representation of 25 as sum of two squares:
PowersRepresentations generates an ordered representation:
Number of representations of a number as a sum of four squares:
Computation by SquaresR:
Properties & Relations (4)
This counts the number of divisors:
In general, DivisorSigma[d,n]==∑k|nkd:
Similarly, EulerPhi[n]==n∏p|n(1-1/p) where p is prime:
Possible Issues (1)
Divisors gives all divisors except for multiplication by units; that is, they lie in the first quadrant:
See Also
FactorInteger EulerPhi Divisible DivisorSigma DivisorSum PerfectNumber
Function Repository: DivisorHasseDiagram
Tech Notes
Related Guides
Related Links
History
Introduced in 1988 (1.0)
Text
Wolfram Research (1988), Divisors, Wolfram Language function, https://reference.wolfram.com/language/ref/Divisors.html.
CMS
Wolfram Language. 1988. "Divisors." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Divisors.html.
APA
Wolfram Language. (1988). Divisors. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Divisors.html
BibTeX
@misc{reference.wolfram_2025_divisors, author="Wolfram Research", title="{Divisors}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Divisors.html}", note=[Accessed: 04-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_divisors, organization={Wolfram Research}, title={Divisors}, year={1988}, url={https://reference.wolfram.com/language/ref/Divisors.html}, note=[Accessed: 04-August-2025]}