Question

hcf of 136,170 and 255​

Answer 1

$\textsf{\large{Answer :-}}$

$\textsf{\large{HCF is 17}}$

$\textsf{\large{Explaination:-}}$

HCF of 136,170 and 255 =

Prime Factorization of 136 =

$\begin{array}{r|l} 2 & 68 \\\cline{1-2} 2 & 34 \\\cline{1-2} 17 & 17\\\cline{1-2} &1\\\end{array}$

Prime Factorization of 170 =

$\begin{array}{r|l}18 & 99 \\\cline{1-2} 2 & 170 \\\cline{1-2} 5 & 85\\ \cline{1-2} 17 & 17 \\\cline{1-2} & 1\end{array}$

Prime Factorization of 255 =

$\begin{array}{r|l}3 & 255 \\\cline{1-2} 5 & 85 \\\cline{1-2} 17 & 17 \\ \cline{1-2} & 1\end{array}$

$\textsf{\large{Factors of 136 }}$

$\tt{ \Rightarrow 2 \times 2 \times 2 \times {\underline{\red{17}}}}$

$\textsf{\large{Factors of 170}}$

$\tt{ \Rightarrow 2 \times 5 \times {\underline{\red{17}}}}$

$\textsf{\large{Factors of 255 }}$

$\tt{\Rightarrow 3 \times 5 \times {\underline{\red{17}}}}$

Common Factor(s )= 17

Highest among the factors = ${\underline{\red{17}}}$

$\therefore$The HCF of 136,170 and 255 is 17