Function Repository Resource:

CommonDivisors

Source Notebook

Find the common divisors of two or more integers

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["CommonDivisors"][{n₁,n₂,…}]

gives the common divisors of the integers n_i.

ResourceFunction["CommonDivisors"][n]

gives the integer divisors of an integer n.

Details and Options

ResourceFunction["CommonDivisors"] works only with integers and Gaussian integers.

The input to ResourceFunction["CommonDivisors"] must be exact, not approximate, numbers.

Examples

Basic Examples (2)

Find the common divisors of a list of integers:

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Find the divisors of a single integer:

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Scope (2)

Find the common divisors of a list of powers:

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CommonDivisors can handle Gaussian integers:

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Applications (1)

Make a table showing that the first five primes share no proper common divisors other than 1:

In[5]:=

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In[6]:=

data = Outer[ResourceFunction["CommonDivisors"][{#1, #2}] &, primes, primes];
headerLines = {Join[{"CommonDiviors[n, m]"}, Table[SpanFromLeft, n - 1]], Prepend[primes, {"n=/m="}]};
Grid[headerLines~Join~Thread[Prepend[data, primes]], Frame -> All, Background -> {{LightGray, None}, {LightPurple, LightGray, {None}}}]

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Possible Issues (1)

The input to CommonDivisors must consist of exact, not approximate, numbers:

In[7]:=

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Publisher

Wolfram|Alpha Math Team

Version History

6.0.0 – 23 March 2023
5.0.0 – 16 April 2020
4.0.0 – 16 April 2020
3.0.0 – 24 January 2020
2.0.0 – 06 September 2019
1.0.0 – 23 July 2019

Related Resources

Author Notes

To view the full source code for CommonDivisors, evaluate the following: