HCF of 210 and 55:
$210 = 55 \times 3 + 45$
$55 = 45 \times 1 + 10$
$45 = 10 \times 4 + 5$
$10 = 5 \times 2 + 0$
∴ HCF(210, 55) = 5
Given: $210 \times 5 + 55m = 5$
$1050 + 55m = 5$
$55m = 5 - 1050 = -1045$
$$m = \frac{-1045}{55} = -19$$
∴ m = −19
Source: Chapter 1, Euclid's Division Algorithm
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The examiner expects you to first find HCF(210, 55) using Euclid's Division Algorithm (step-by-step), then substitute it into the given expression and solve for m. Both steps carry marks — don't skip the division steps. The negative value of m is correct and expected.