Ta có:105 chia hết cho a

\(\Rightarrow a\inƯ\left(105\right)=\left\{1;3;5;7;15;21;35;105\right\}\)

Vì \(16\le a\le50\)nên \(a\in\left\{21;35\right\}\)

Vậy \(a\in\left\{21;35\right\}\)

105=3.5.7

a=3.5=15 hoặc 3.7=21 hoặc 5.7=35 mà 15<a<50
=> a\(\in\){21;35}

Vì 105 ⋮ a nên a ∈ Ư ( 105 ) = { 1 ; 3 ; 5 ; 7 ; 15 ; 35 ; 105 }

Vì 16 < a < 50 nên a = 35

Vậy a = 35 

a: \(50=2\cdot5^2;75=5^2\cdot3\)

=>\(ƯCLN\left(50;75\right)=5^2=25\)

=>\(ƯC\left(50;75\right)=Ư\left(25\right)=\left\{1;5;25\right\}\)

\(x\inƯC\left(50;75\right)\)

=>\(x\in\left\{1;5;25\right\}\)

mà x<=20

nên \(x\in\left\{1;5\right\}\)

b: \(35=5\cdot7;105=3\cdot5\cdot7\)

=>\(ƯCLN\left(35;105\right)=5\cdot7=35\)

\(35⋮x;105⋮x\)

=>\(x\inƯC\left(35;105\right)\)

=>\(x\inƯ\left(35\right)\)

=>\(x\in\left\{1;5;7;35\right\}\)

mà x>5

nên \(x\in\left\{7;35\right\}\)

c: \(144=2^4\cdot3^2;192=2^6\cdot3;240=2^4\cdot3\cdot5\)

=>\(ƯCLN\left(144;192;240\right)=2^4\cdot3=48\)

\(144⋮x;192⋮x;240⋮x\)

=>\(x\inƯC\left(144;192;240\right)\)

mà x lớn nhất

nên x=ƯCLN(144;192;240)=48

d: \(54=3^3\cdot2;14=2\cdot7\)

=>\(ƯCLN\left(54;14\right)=2\)

\(x\inƯC\left(54;14\right)\)

mà x lớn nhất

nên x=ƯCLN(54;14)

=>x=2