НОД(16;24) = 8
$16 = 2^4$
$ \begin{array}{r|l} 16 & 2\\ 8 & 2\\ 4 & 2\\ 2 & 2\\ 1 & \end{array} $
$24 = 2^3 * 3$
$ \begin{array}{r|l} 24 & 2\\ 12 & 2\\ 6 & 3\\ 2 & 2\\ 1 & \end{array} $

НОД(15;60) = 15
$15 = 3 * 5$
$ \begin{array}{r|l} 15 & 3\\ 5 & 5\\ 1 & \end{array} $
$60 = 2^2 * 3 * 5$
$ \begin{array}{r|l} 60 & 2\\ 30 & 2\\ 15 & 5\\ 3 & 3\\ 1 & \end{array} $

НОД(10;15) = 5
$10 = 2 * 5$
$ \begin{array}{r|l} 10 & 2\\ 5 & 5\\ 1 & \end{array} $
$15 = 3 * 5$
$ \begin{array}{r|l} 15 & 3\\ 5 & 5\\ 1 & \end{array} $

НОД(45;56) = 1
$45 = 3^2 * 5$
$ \begin{array}{r|l} 45 & 3\\ 15 & 3\\ 5 & 5\\ 1 & \end{array} $
$56 = 2^3 * 7$
$ \begin{array}{r|l} 56 & 2\\ 28 & 2\\ 14 & 2\\ 7 & 7\\ 1 & \end{array} $

НОД(21;49) = 7
$21 = 3 * 7$
$ \begin{array}{r|l} 21 & 3\\ 7 & 7\\ 1 & \end{array} $
$49 = 7 * 7$
$ \begin{array}{r|l} 49 & 7\\ 7 & 7\\ 1 & \end{array} $

НОД(12;18;24) = 6
$12 = 2^2 * 3$
$ \begin{array}{r|l} 12 & 2\\ 6 & 2\\ 3 & 3\\ 1 & \end{array} $
$18 = 2 * 3^2$
$ \begin{array}{r|l} 18 & 2\\ 9 & 3\\ 3 & 3\\ 1 & \end{array} $
$24 = 2^3 * 3$
$ \begin{array}{r|l} 24 & 2\\ 12 & 2\\ 6 & 2\\ 3 & 3\\ 1 & \end{array} $