The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
The factors that are on both lists ... the "common" factors ... are 1, 2, 3, and 6 .
The greatest one of those is 6 .
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Because 6 is the largest positive integer that divides evenly into both 18 and 30 with no remainder.