Exercise 1: Tracing the Euclidean Algorithm for GCD(252, 105) — Possible Solution
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GIVEN
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a = 252, b = 105

STEP-BY-STEP TRACE
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252 = 105*2 + 42   -> next pair (105, 42)
105 = 42*2 + 21    -> next pair (42, 21)
42  = 21*2 + 0     -> remainder 0, stop

RESULT
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GCD(252, 105) = 21

Confirming: 252 / 21 = 12 exactly, and 105 / 21 = 5 exactly, so 21
does divide both numbers, and no larger number could (the
algorithm's own correctness guarantee, proved in this chapter,
means the last non-zero value genuinely is the greatest common
divisor, not just a common divisor).

WHY THIS WORKS AS AN ANSWER
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Each step is shown in the exact a = b*q + r form this chapter uses,
with the pair correctly updated to (b, r) at each stage, and the
algorithm is run all the way to a zero remainder rather than
stopped early.