Vì ƯCLN ( a , b ) = 4
Nên a = m . n ; b = 4 . n (m, n ) = 1
Mà a . b = 384 hay 4 . m . 4 . n = 384
16 . ( m . n ) = 384
m . n = 384 : 16
m . n = 24 (m, n ) = 1
Nếu m > n => a > b (m, n ) = 1
=> (m , n) ϵ { (24 ; 1) ; ( 8 ; 3 ) }
Ta có bảng sao :
| m | 24 | 8 |
| n | 1 | 3 |
| a | 96 | 24 |
| b | 4 | 12 |
Vậy (a, b) ϵ { (96 ; 4) ; ( 24 ; 12) }
\(\left[{}\begin{matrix}\left\{{}\begin{matrix}a=96\\b=4\end{matrix}\right.\\\left\{{}\begin{matrix}a=4\\b=96\end{matrix}\right.\\\left\{{}\begin{matrix}a=12\\b=32\end{matrix}\right.\\\left\{{}\begin{matrix}a=32\\b=12\end{matrix}\right.\end{matrix}\right.\)
