Theo đề bài, ta có:
332 : a dư 17 => 332 - 17 = 315 \(⋮\) a ( a > 17 )
555 : a dư 15 => 555 - 15 = 540 \(⋮\) a ( a > 15 )
\(\Rightarrow a\inƯC\left(315;540\right)\)
Ta có: \(315=3^2.5.7\)
\(540=2^2.3^2.5\)
\(\RightarrowƯC=\left\{315;540\right\}=3^2.5=45\)
\(\RightarrowƯC\left(315;540\right)=Ư\left(45\right)=\left\{1;3;5;9;15;45\right\}\)
Vì a > 17 nên a = 45
Vậy a = 45