Question

) Find the HCF of 180 and 204 using the common factor method. ​

Answer 1

Step-by-step explanation:

Find the prime factorization of 180. 180 = 2 × 2 × 3 × 3 × 5.

Find the prime factorization of 204. 204 = 2 × 2 × 3 × 17.

Therefore, = 2 × 2 × 3.

= 12.

Answer 2

$\LARGE\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:180 \:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:90 \:\:}} \\\underline{\sf{3}}&\underline{\sf{\:\:45\:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\:\:15 \:\:}} \\ {\underline{\sf{5}}}& \underline{\sf{\:\:5\:\:}}\\ {\underline{\sf{}}}& \underline{\sf{\:\:1\:\:}}\\\end{array}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$= \tt{2 \times 2 \times 3 \times 3 \times 5 \times 1}$

$\LARGE\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:204 \:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:102 \:\:}} \\\underline{\sf{3}}&\underline{\sf{\:\:51\:\:}} \\ {\underline{\sf{17}}}& \underline{\sf{\:\:17\:\:}} \\ {\underline{\sf{}}}& \underline{\sf{\:\:1\:\:}}\\ \end{array}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$= \tt{2 \times 2 \times 3 \times 17 \times 1}$

$= \tt{ {2}^{2} \times {3}^{2} \times 5 \times \red1}$

$= \tt{ {2}^{2} \times 3 \times 17 \times \red 1}$

$\tt{HCF=1}$