Example 11.31: gcd(24, 36, 54) = 6, because 24/6, 36/6, and 54/6 each have remainder 0, yet any integer larger than 6 must leave a nonzero remainder when dividing at least one of 24, 36, and 54. For instance, 12 divides 24 and 36 evenly, but not 54.
The importance of the GCD is in the following theorem.Example