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Number Theory Guide

Number Theory Level 12: GCD (<= 120). Euclidean algorithm.

1. First Euclid step

1. First Euclid step
Replace the pair with divisor and remainder.

Replace the larger number with its remainder.

96 = 84 + 12.

2. Repeat with remainder

2. Repeat with remainder
First Euclid step

Continue until the smaller number divides exactly.

84 = 12 x 7.

3. Read GCD

3. Read GCD
First Euclid step
Repeat with remainder

The last nonzero divisor is the GCD.

GCD = 12.