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The invariant property is that the set of common divisors of two numbers $a$ and $b$ is identical to the set of common divisors of $a$ and $b-a$ (or $b$ and $a \bmod b$). This ensures that the greatest common divisor (gcd) remains unchanged throughout the algorithm's steps.

Conditions: $a$ and $b$ are integers.; The operation is either subtraction ($b-a$) or modulo ($a \bmod b$).

The invariant property is that the set of common divisors of two numbers $a$ and $b$ is identical to the set of common divisors of $a$ and $b-a$ (or $b$ and $a \bmod b$). This ensures that the greatest common divisor (gcd) remains unchanged throughout the algorithm's steps.

Conditions: $a$ and $b$ are integers.; The operation is either subtraction ($b-a$) or modulo ($a \bmod b$).