Help with number theory. If a and b are integers, not both zero, then an integer d is called the greatest common divisor of a and b if
i) d > 0
ii) d is a common divisor of a and b; and
iii) each integer m that is a divisor of a and b is also a divisor of d.
explain the third (iii) criteria. How does it capture the idea that d is the greatest among the common divisors?

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iii translates to
\(c\mid a\) and \(c\mid b\) \(\implies c\mid \gcd(a,b)\)

That means every common divisor of \(a\) and \(b\) is also a divisor of \(\gcd(a,b)\)

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