C :

#include<stdio.h>
#include<string.h>
int main()
{
	char buf[90];
	gets(buf);
	int i,j,first;
	for(i=1;;i++)
	{
		first=1;
		for(j=i;j<strlen(buf);j++)
		{
			if(buf[j]!=buf[j-i]){first=0;break;}
		}
		if(first){printf("%d",i);break;}
	}
	return 0;
} 

C++ :

#include <cstdio>
#include <iostream>
#include <cstring>
using namespace std;
int main()
{
  char word[101];
  scanf("%s", word);
  int len = strlen(word);
  for (int i = 1; i <= len; i=i+1) 
  if (len % i == 0) {
        int ok = 1;
        for (int j = i; j < len; ++j)
            if (word[j] != word[j % i]) { ok = 0; break; }
        if (ok) { printf("%d\n", i); break; }
  }
  return 0;

}