Question 442696
Let n = 88p  + 8
    n/88 = p + 1/11
    
    n = 11q +  r
    n/11 = q+ r/11
    n/88 = q/8 + r/88

    p+1/11 = q/8 + r/88

    p+8/88 = q/8 + r/88

    so {{{q>=8}}}
    
    We know p = (11q +r -8 /88)

    The only way for (11q+r-8)/88  is that we have (11q/88) or (11q-11)/88
    So r = -3 or r = 8.  

    Since 0<r<11, then r=8.

    The remainder would be 8.