Question

Find the HCF
of 18, 50 and 72 by prime factorisation. ​

Answer 1

Answer:

Prime factorisation of the given numbers are :

54=2×3×3×3

72=2×2×2×3×3

90=2×3×3×5

Notice that 2 occurs as a common prime factor at least one times and 3 at least two times in given numbers.

∴ H.C.F =2×3×3=18

Answer 2

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:18\:\:}}}\\ {\underline{\sf{3}}}& \underline{\sf{\:\:9 \:\:}} \\\underline{\sf{3}}&\underline{\sf{\:\:3\:\:}} \\ {\underline{\sf{}}}& \underline{\sf{\:\:1 \:\:}}\end{array} \end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\tt{18 = 2 \times 3 \times 3}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:50\:\:}}}\\ {\underline{\sf{5}}}& \underline{\sf{\:\: 25\:\:}} \\\underline{\sf{5}}&\underline{\sf{\:\:5\:\:}} \\ {\underline{\sf{}}}& \underline{\sf{\:\:1 \:\:}}\end{array} \end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\tt{50 = 2 \times 5 \times 5}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:72\:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\: 36\:\:}} \\\underline{\sf{2}}&\underline{\sf{\:\:18\:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\:\:9 \:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\:\:3\:\:}} \\ {\underline{\sf{}}}& \underline{\sf{\:\:1\:\:}}\end{array} \end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\tt{72 =2 \times 2 \times 2 \times 3 \times 3}$

$\tt{18 = \orange 2 \times {3}^{2} }$

$\tt{50 = \orange2 \times {5}^{2} }$

$\tt{72 = \orange2\times {2}^{2} \times {3}^{2} }$

$\tt{HCF= \orange2}$