Harmonic Product Spectrum algorithm. I dont understand one step I was looking some Harmonic Product Spectrum algorithm examples and I came up with this:

//Implement Harmonic Product Spectrum
for(k = 0; k &lt; buffer_size / 8; k++)
{
    sum[k] = magFFT[k] * magFFT[2*k] * magFFT[3*k];
    // find fundamental frequency (maximum value in plot)
    if( sum[k] &gt; max_value2 &amp;&amp; k &gt; 0 )
    {
        max_value2 = sum[k];
        fund_freq = k;
    }
 }
 fund_freq1 = fund_freq * 8000 / buffer_size;


What I dont understand is the reason behind the last line, I tested it and it works but I couldn't find an explanation for that multiplication. Can anyone help me please? 

Source of code: SOURCE
"8000 / buffer_size"  is frequency resolution, decide by  sample length or "buffer_size",

you know the sampling interval is "1/8000", the whole time length 'T' of the sequence is "buffer_size/8000", then '1/T' is frequency resolution, 

in your code,if 'k' is 0, represent 0hz,is the signal's dc part,if 'k' is 1,represent '1/T' or "8000 / buffer_size" hz, then you can see 'k' correspond with frequency bin "k*8000 / buffer_size" .