Đáp án:
1) $x=4$
3) $x=14$
4) $x=\{1,2,3,6\}$
Giải thích các bước giải:
1)
$24$ $\vdots$ $x\Rightarrow x\in Ư(24)$
$36$ $\vdots$ $x\Rightarrow x\in Ư(36)$
$160$ $\vdots$ $x\Rightarrow x\in Ư(160)$
$\Rightarrow x\in ƯC(24,36,160)$
Do $x$ lớn nhất nên $x=ƯCLN(24,36,160)$
Ta có: $24=2^3.3$
$36=2^2.3^2$
$160=2^5.5$
$\Rightarrow ƯCLN(24,36,160)=2^2=4$
Vậy $x=4$
3)
$70$ $\vdots$ $x\Rightarrow x\in Ư(70)$
$84$ $\vdots$ $x\Rightarrow x\in Ư(84)$
$\Rightarrow x\in ƯC(70,84)$
Ta có: $70=2.5.7$
$84=2^2.3.7$
$\Rightarrow ƯCLN(70,84)=2.7=14$
$\Rightarrow ƯC(70,84)=\{1,2,7,14\}$
Do $x>8\Rightarrow x=14$
4)
$150$ $\vdots$ $x\Rightarrow x\in Ư(150)$
$84$ $\vdots$ $x\Rightarrow x\in Ư(84)$
$30$ $\vdots$ $x\Rightarrow x\in Ư(30)$
$\Rightarrow x\in ƯC(150,84,30)$
Ta có: $150=2.3.5^2$
$84=2^2.3.7$
$30=2.3.5$
$\Rightarrow ƯCLN(150,84,30)=2.3=6$
$\Rightarrow ƯC(70,84)=\{1,2,3,6\}$
Do $0<x<16\Rightarrow x=\{1,2,3,6\}$
