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お世話になります。
連続しての質問で恐縮です。
OGの解説に(2)がsufficientである説明があるのですが、何のことやらさっぱりわかりません（特に12 が x と y の公約数になるあたりの理屈がわかりません）。どなたか説明をお願いできませんでしょうか？
If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y ?
(1) x = 12u , where u is an integer.
(2) y = 12z , where z is an integer.
（OG 解説）
Statement (2) implies that y is a multiple of 12 or that 12 is a divisor of y. Since x = 8y + 12, it follows that 12 is a divisor of x, and thus 12 is a common divisor of x and y must be a divisor of 12. Therefore no integer greater than 12 is a common divisor of x and y, and 12 is the greatest common divisor of x and y.
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