Question

lf the h.c.f of 192 and 132 can be represented as fallow , what will be the value of p,?​

Answer 1

Answer:

12

Step-by-step explanation:

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Answer 2

Note: The question is incomplete as it should be, "If HCF of $192$ and $132$ can be repesented as $5p-8$. then find the value of $p.$"

Given:

Expression for the HCF of $192$ and $132$ $=5p-8$.

To find: The value of $p.$

Solution:

Find the HCF of $192$ and $132$.

$192=\[2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3\]$

     $\[ = {2^6} \times 3\]$

$132=\[2 \times 2 \times 3 \times 11\]$

     $\[ = {2^2} \times 3 \times 11\]$

HCF$\[\left( {192,132} \right) = {2^2} \times 3\]$

                      $\[ = 12\]$

Find the value of $p.$

Equate the given expression for the HCF of $192$ and $132$ and the HCF calculated.

$\[5p - 8 = 12\]$

$\[ \Rightarrow 5p = 12 + 8\]$

$\[ \Rightarrow 5p = 20\]$

$\[ \Rightarrow p = \frac{{20}}{5}\]$

$\[ \Rightarrow p = 4\]$

Hence, the value of $p$ is $4.$