Vì 126 chia hết cho x , 210 chia hết cho x nên x ƯC(126,210)
Ta có : 126 = 2 . 3
2 . 7 ; 210 = 2 . 3 . 5 . 7
=> ƯCLN(126,210) = 2 . 3 . 7 = 42
Mà Ư(42) = {1;2;3;6;7;14;21;42}
=> ƯC(126,210) = {1;2;3;6;7;14;21;42}
=> x {1;2;3;6;7;14;21;42}
Vì 15 < x < 30 nên x = 21
Vậy x = 21
chúc bn học tốt nha
\(\hept{\begin{cases}126⋮x\\210⋮x\end{cases}\Rightarrow x\inƯC\left(126;210\right)}\) (1)
ta có :
126 = 2.63 = 2.32.7
210 = 3.70 = 2.3.5.7
nên :
ƯCLN(126; 210) = 2.3.7 = 42
ƯC(126; 210) = Ư(42) = {1; 2; 3; 6; 7; 14; 21; 42} (2)
15 < x < 30 (3)
(1)(2)(3) => x = 21
\(\text{Bài giải }\)
\(\hept{\begin{cases}126\text{ }⋮\text{ }x\\210\text{ }⋮\text{ }x\end{cases}\Rightarrow\text{ }\inƯC\left(126\text{ };\text{ }210\right)}\) \(\left(1\right)\)
\(\text{Ta có : }\)
\(126=2\cdot63=2\cdot3^2\cdot7\)
\(210=3\cdot70=2\cdot3\cdot5\cdot7\)
\(\text{Nên : }\)
\(ƯCLN\left(126\text{ };\text{ }210\right)=2\cdot3\cdot7=42\)
\(ƯC\left(126\text{ ; }210\right)=Ư\left(42\right)=\left\{1\text{ ; }2\text{ ; }3\text{ ; }6\text{ ; }7\text{ ; }14\text{ ; }21\text{ ; }42\right\}\) \(\left(2\right)\)
\(15< x< 30\) \(\left(3\right)\)
\(\left(1\right)\left(2\right)\left(3\right)\Rightarrow\text{ }x=21\)
