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# 1. Find the HCF of the following numbers : (a) 18, 48 (b) 30, 42 (c) 18, 60 (d) 27, 63 (e) 36, 84 (f) 34, 102 (g) 70, 105, 175 (h) 91, 112, 49 (i) 18, 54, 81 (j) 12, 45, 75

(a) 18, 48 $$\begin{array}{|l} \llap{2~~~~} 18 \\ \hline \llap{3~~~~} 9 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{2~~~~} 48 \\ \hline \llap{2~~~~} 24 \\ \hline \llap{2~~~~} 12 \\ \hline \llap{2~~~~} 6 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array}$$ 18 = 2 × 3 × 3
48 = 2 × 2 × 2 × 2 × 3
HCF = 2 × 3 = 6
(b) 30, 42 $$\begin{array}{|l} \llap{2~~~~} 30 \\ \hline \llap{3~~~~} 15 \\ \hline \llap{5~~~~} 5 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{2~~~~} 42 \\ \hline \llap{3~~~~} 21 \\ \hline \llap{7~~~~} 7 \\ \hline 1 \end{array}$$ 30 = 2 × 3 × 5
42 = 2 × 3 × 7
HCF = 2 × 3 = 6
(c) 18, 60
$$\begin{array}{|l} \llap{2~~~~} 18 \\ \hline \llap{3~~~~} 9 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{2~~~~} 60 \\ \hline \llap{2~~~~} 30 \\ \hline \llap{3~~~~} 15 \\ \hline \llap{5~~~~} 5 \\ \hline 1 \end{array}$$ 18 = 2 × 3 × 3
60 = 2 × 2 × 3 × 5
HCF = 2 × 3 = 6
(d) 27, 63
$$\begin{array}{|l} \llap{3~~~~} 27 \\ \hline \llap{3~~~~} 9 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{3~~~~} 63 \\ \hline \llap{7~~~~} 21 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array}$$ 27 = 3 × 3 × 3
63 = 3 × 3 × 7
HCF = 3 × 3 = 9
(e) 36, 84 $$\begin{array}{|l} \llap{2~~~~} 36 \\ \hline \llap{2~~~~} 18 \\ \hline \llap{3~~~~} 9 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{2~~~~} 84 \\ \hline \llap{2~~~~} 42 \\ \hline \llap{3~~~~} 21 \\ \hline \llap{7~~~~} 7 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{2~~~~} 36 \\ \hline \llap{2~~~~} 18 \\ \hline \llap{3~~~~} 9 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{2~~~~} 84 \\ \hline \llap{2~~~~} 42 \\ \hline \llap{3~~~~} 21 \\ \hline \llap{7~~~~} 7 \\ \hline 1 \end{array}$$ 36 = 2 × 2 × 3 × 3
84 = 2 × 2 × 3 × 7
HCF = 2 × 2 × 3 = 12
(f) 34, 102 $$\begin{array}{|l} \llap{2~~~~} 34 \\ \hline \llap{17~~~~} 17 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{2~~~~} 102 \\ \hline \llap{3~~~~} 51 \\ \hline \llap{17~~~~} 17 \\ \hline 1 \end{array}$$ 34 = 2 × 17
102 = 2 × 3 × 17
HCF = 2 × 17 = 34
(g) 70, 105, 175 $$\begin{array}{|l} \llap{2~~~~} 70 \\ \hline \llap{5~~~~} 35 \\ \hline \llap{7~~~~} 7 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{3~~~~} 105 \\ \hline \llap{5~~~~} 35 \\ \hline \llap{7~~~~} 7 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{5~~~~} 175 \\ \hline \llap{5~~~~} 35 \\ \hline \llap{7~~~~} 7 \\ \hline 1 \end{array}$$ 70 = 2 × 5 × 7
105 = 3 × 5 × 7
175 = 5 × 5 × 7
HCF = 5 × 7 = 35
(h) 91, 112, 49 $$\begin{array}{|l} \llap{7~~~~} 91 \\ \hline \llap{13~~~~} 13 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{2~~~~} 112 \\ \hline \llap{2~~~~} 56 \\ \hline \llap{2~~~~} 28 \\ \hline \llap{2~~~~} 14 \\ \hline \llap{7~~~~} 7 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{7~~~~} 49 \\ \hline \llap{7~~~~} 7 \\ \hline 1 \end{array}$$ 91 = 7 × 13
112 = 2 × 2 × 2 × 2 × 7
49 = 7 × 7
HCF = 7
(I) 18, 54 , 81 $$\begin{array}{|l} \llap{2~~~~} 18 \\ \hline \llap{3~~~~} 9 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{2~~~~} 54 \\ \hline \llap{3~~~~} 27 \\ \hline \llap{3~~~~} 9 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{3~~~~} 81 \\ \hline \llap{3~~~~} 27 \\ \hline \llap{3~~~~} 9 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{2~~~~} 18 \\ \hline \llap{3~~~~} 9 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array}$$ 18 = 2 × 3 × 3
54 = 2 × 3 × 3 × 3
81 = 3 × 3 × 3 × 3
HCF = 3 × 3 = 9
(i) 12, 45, 75 $$\begin{array}{|l} \llap{2~~~~} 12 \\ \hline \llap{2~~~~} 6 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{3~~~~} 45 \\ \hline \llap{3~~~~} 15 \\ \hline \llap{5~~~~} 5 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{3~~~~} 75 \\ \hline \llap{5~~~~} 25 \\ \hline \llap{5~~~~} 5 \\ \hline 1 \end{array}$$ 12 = 2 × 2 × 3
45 = 3 × 3 × 5
75 = 3 × 5 × 5
HCF = 3