\[\boxed{\mathbf{1.}}\]
\[1)\ 150\ :30 =\]
\[= (150\ :10)\ :(30\ :10) =\]
\[= 15\ :3 = 5\]
\[2)\ 75\ 000\ :2500 =\]
\[= (75\ 000\ :100)\ :(2500\ :100) =\]
\[= 750\ :25 = 30\]
\[\boxed{\mathbf{2.}}\]
\[1)\ 205\ :5 = (205 \cdot 2)\ :(5 \cdot 2) =\]
\[= 210\ :10 = 21\]
\[2)\ 325\ :5 = (325 \cdot 2)\ :(5 \cdot 2) =\]
\[= 650\ :10 = 65\]
\[\boxed{\mathbf{3.}}\]
\[1)\ (600 + 21)\ :3 =\]
\[= 600\ :3 + 21\ :3 =\]
\[= 200 + 7 = 207\]
\[2)\ 432\ :4 = (400 + 32)\ :4 =\]
\[= 400\ :4 + 32\ :4 = 100 + 8 =\]
\[= 108\]
\[3)\ 574\ :7 = (560 + 14)\ :7 =\]
\[= 560\ :7 + 14\ :7 =\]
\[= 80 + 2 = 82\]
\[4)\ 288\ :8 = (240 + 48)\ :8 =\]
\[= 240\ :8 + 48\ :8 =\]
\[= 30 + 6 = 36\]