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Find the greatest number which divides $764$ and $1198$, leaving remainders $8$ and $10$ respectively.
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$764-8=756$ and $1198-10 = 1188$ (I) (1 Mark)
$756 = 2^2 \times 3^3 \times 7$ (II) (1/2 Mark)
$1188 = 2^2 \times 3^3 \times 11$ (III) (1/2 Mark)
H.C.F. $(756, 1188) = 2^2 \times 3^3 = 108$ (IV) (1 Mark)
$\therefore$ Required greatest number is $108$.
$756 = 2^2 \times 3^3 \times 7$ (II) (1/2 Mark)
$1188 = 2^2 \times 3^3 \times 11$ (III) (1/2 Mark)
H.C.F. $(756, 1188) = 2^2 \times 3^3 = 108$ (IV) (1 Mark)
$\therefore$ Required greatest number is $108$.