Example 1:
$$ \textup{Find the H.C.F. of } 24 \textup{ and } 42 $$
Solution:
$$
\begin{array}{|l}
\llap{2~~~~} 24,42 \\ \hline
\llap{3~~~~} 12,21 \\ \hline
\phantom{x}4,7
\end{array}
$$
$$ \textup{H.C.F. }=2×3$$
$$ \textup{H.C.F. }=6$$
Example 2:
$$ \textup{Find the H.C.F. of } 220 \textup{ and } 275 $$
Solution:
$$
\begin{array}{|l}
\llap{5~~~~} 220,275\\ \hline
\llap{11~~~~} 44,55\\ \hline
\phantom{x}4,5
\end{array}
$$
$$ \textup{H.C.F. }=5×11$$
$$ \textup{H.C.F. }=55$$
Example 1:
$$ \textup{Find the H.C.F. of } 60 \textup{ and } 84 $$
Solution:
$$
\begin{array}{|l}
\llap{2~~~~} 60,84 \\ \hline
\llap{2~~~~} 30,42 \\ \hline
\llap{3~~~~} 15,21 \\ \hline
\phantom{x}5,7
\end{array}
$$
$$ \textup{H.C.F. }=2×2×3$$
$$ \textup{H.C.F. }=12$$
Example 2:
$$ \textup{Find the H.C.F. of } 126 \textup{ and } 294 $$
Solution:
$$
\begin{array}{|l}
\llap{2~~~~} 126,294 \\ \hline
\llap{3~~~~} 63,147 \\ \hline
\llap{7~~~~} 21,49 \\ \hline
\phantom{x}3,7
\end{array}
$$
$$ \textup{H.C.F. }=2×3×7$$
$$ \textup{H.C.F. }=42$$
Example 1:
$$ \textup{Find the H.C.F. of } 420 \textup{ and } 660 $$
Solution:
$$
\begin{array}{|l}
\llap{2~~~~} 420,660 \\ \hline
\llap{2~~~~} 210,330 \\ \hline
\llap{3~~~~} 105,165 \\ \hline
\llap{5~~~~} 35,55 \\ \hline
\phantom{x}7,11
\end{array}
$$
$$ \textup{H.C.F. }=2×2×3×5$$
$$ \textup{H.C.F. }=60$$
Example 2:
$$ \textup{Find the H.C.F. of } 252 \textup{ and } 468$$
Solution:
$$
\begin{array}{|l}
\llap{2~~~~} 252,468 \\ \hline
\llap{2~~~~} 126,234 \\ \hline
\llap{3~~~~} 63,117\\ \hline
\llap{3~~~~} 21,39 \\ \hline
\phantom{x}7,13
\end{array}
$$
$$ \textup{H.C.F. }=2×2×3×3$$
$$ \textup{H.C.F. }=36$$