请教:Y=3K从哪儿变出来的?

xulingyan

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
the key is D. How to deal with this kind of question.
由题知: x=4(2y+3)
   由(1)知: x=12u 则y=3k k is an integer. x=12(2k+1) 则x,y最大公因子不能确定.
   由(2)知: y=12z 则x=12(6z+1) ,因此x,y的公因子是12。
    这题我认为选B

请教:Y=3K从哪儿变出来的?数学太菜,不好意思

xulingyan

明白了,谢谢

自尊宝

x=12u

12u=8y+12

u=2y/3 + 1, u is positive integer, =>y=3k