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If the HCF of $210$ and $55$ is expressed as $210 \times 5 + 55m$, then find the value of $m$.
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Sol. $210 = 2 \times 3 \times 5 \times 7$
$55 = 5 \times 11$
H.C.F. $(210, 55) = 5$ (I) (1 Mark)
$\therefore 5 = 210 \times 5 + 55m$ (II) ($\frac{1}{2}$ Mark)
$\Rightarrow m = -19$ (III) ($\frac{1}{2}$ Mark)
$55 = 5 \times 11$
H.C.F. $(210, 55) = 5$ (I) (1 Mark)
$\therefore 5 = 210 \times 5 + 55m$ (II) ($\frac{1}{2}$ Mark)
$\Rightarrow m = -19$ (III) ($\frac{1}{2}$ Mark)