Rotational symmetry of string A rotation "is made by splitting a string into two pieces and reversing their order". An object is symmetrical under an operation if the object is unchanged after applying said operation. So, a "rotational symmetry" is the fact that a string remains unchanged after "rotation".

Given a non-empty string s consisting of only letters from a to z, output the highest order of the rotational symmetry of the string.

Testcases:

input        output
a            1
abcd         1
abab         2
dfdfdfdfdfdf 6


This is code-golf. Shortest answer in bytes wins. Standard loopholes apply.
Retina, 15 bytes

(^.+?|\1)+$
$#1


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Matches the entire string by repeating a substring (shorter substrings are prioritised due to the ungreedy .+?) and replaces the entire string with the number of repetitions we used.