Question

Tìm a,b biết a.b =150 ; UCLN(a,b)=5

Answer 1

Vì \(ƯCLN\left(a,b\right)=5\Rightarrow\left\{{}\begin{matrix}a=5k\\b=5q\end{matrix}\right.\left(k,q\in N\text{*}\right)\)

Ta có \(ab=150\Rightarrow25kq=150\Rightarrow kq=6\)

Mà \(\left(k,q\right)=1\)

\(\Rightarrow\left(k,q\right)\in\left\{\left(1;6\right);\left(6;1\right);\left(2;3\right);\left(3;2\right)\right\}\\ \Rightarrow\left(a;b\right)\in\left\{\left(5;30\right);\left(30;5\right);\left(10;15\right);\left(15;10\right)\right\}\)