<p>For two strings <code>s</code> and <code>t</code>, we say &quot;<code>t</code> divides <code>s</code>&quot; if and only if <code>s = t + t + t + ... + t + t</code> (i.e., <code>t</code> is concatenated with itself one or more times).</p>

<p>Given two strings <code>str1</code> and <code>str2</code>, return <em>the largest string </em><code>x</code><em> such that </em><code>x</code><em> divides both </em><code>str1</code><em> and </em><code>str2</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> str1 = &quot;ABCABC&quot;, str2 = &quot;ABC&quot;
<strong>Output:</strong> &quot;ABC&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> str1 = &quot;ABABAB&quot;, str2 = &quot;ABAB&quot;
<strong>Output:</strong> &quot;AB&quot;
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> str1 = &quot;LEET&quot;, str2 = &quot;CODE&quot;
<strong>Output:</strong> &quot;&quot;
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= str1.length, str2.length &lt;= 1000</code></li>
	<li><code>str1</code> and <code>str2</code> consist of English uppercase letters.</li>
</ul>

class Solution {
public:
    string gcdOfStrings(string str1, string str2) {
        // go through both str, find common substring from index 0 until a mismatch happend
        int i = 0;
        string gcd = "";
        string greatestGcd = "";
        while(i < str1.length() && i < str2.length()){
            if(str1[i] != str2[i]) break;
            gcd += str1[i];
            if(checkGcd(gcd, str1, str2)) greatestGcd = gcd;
            i++;
        }

        return  greatestGcd;
    }

    bool checkGcd(string& gcd, string& s1, string& s2){
        //cout << gcd << endl << s1 << endl << s2 << endl;
        //cout << endl;
        if(s1.length() % gcd.length() != 0 || s2.length() % gcd.length() != 0) return false;

        for(int i=0; i<s1.size(); i+=gcd.size()){
            if(s1.substr(i, gcd.size()) != gcd) return false;
        }

        for(int i=0; i<s2.size(); i+=gcd.size()){
            if(s2.substr(i, gcd.size()) != gcd) return false;
        }

        return true;
    }
};
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