Question

find the HCF of 1
36, 170 and 255 by the prime factorization method​

Answer 1

Answer :

The HCF of 136, 170 and 255 is 17.

Step-by-step explanation :

Given values :

• 136.
• 170.
• 255.

To Find :

HCF of 136, 170 and 255 by the prime factorization method​.

Solution :

We have to factorize the numbers first so,

★ 136 :

$\begin{array}{r|l} 2 & 136 \\ \cline{1-2} 2 & 68 \\\cline{1-2} 2 & 34 \\\cline{1-2} 17 & 17 \\\cline{1-2} & 1 \end{array}$

★ 170 :

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

★ 255 :

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

$\rule{300}{1.5}$

Now, Write the factors together,

★ 136 = 2 × 2 × 2× 17✔️

★ 170 = 2× 5 × 17✔️

★ 255 = 3 × 5 × 17✔️

In these factors the common number is 17.

$\bigstar\;\textbf{\underline{\underline{Hence,The HCF of 136, 170 and 255 is 17.}}}$

Answer 2

$\huge\underline\mathfrak\purple{Answer}$

$\huge\boxed{HCF\:=\:17}$

____________________

$\huge\underline\mathfrak\purple{Explanation}$

To find : The HCF of 136, 170, 255 by prime factorisation method.

Solution : Firstly, we have to find out the prime factors of the following numbers.

[ Refer to the attachment ]

____________________

Now,

The prime factors of 136 are : 2 × 2 × 2 × $\boxed{17}$

The prime factors of 170 are : 2 × 5 × $\boxed{17}$

The prime factors of 255 are : 3 × 5 × $\boxed{17}$

____________________

Therefore, highest common factor (HCF) of 136, 170 and 255 is 17.