Question

HCF of 408 and 1032 is expressed as 1032 ×2+408×p find value of p

Answer 1

Answer:

P= -5.

Given:

The HCF of 408 and 1032 is express as 1032 2 + 408p

Solution:

$\begin{array}{r | l}</p><p></p><p>2 & 1032 \\</p><p></p><p>\cline{2-2} 2 & 516 \\</p><p></p><p>\cline{2-2} 2 & 258 \\</p><p></p><p>\cline{2-2} 3 & 129 \\</p><p></p><p>\cline{2-2} 43 & 43 </p><p>\end{array}$

$\begin{array}{r | l}</p><p></p><p>2 & 408 \\</p><p></p><p>\cline{2-2} 2 & 204 \\</p><p></p><p>\cline{2-2} 2 & 102 \\</p><p></p><p>\cline{2-2} 3 & 51 \\</p><p></p><p>\cline{2-2} 17 & 17</p><p>\end{array}$

$\tt{Common \: factor(1032)}$

$\: \: \: \: \: \: \tt{2 \times 2 \times 2 \times 3} = {2}^{3} \times 3.$

$\tt{Common \: factor (408)}$

$\: \: \: \: \: \: \tt{2 \times 2 \times 2 \times 3 = {2}^{3} \times 3.}$

The HCF of (1032, 408) be 24.

$\rule{200}3$

Now,

$\leadsto \tt{1032 \times 2 + 408p = 24.}$

$\leadsto \tt{ 408p = 24 - 1032 \times 2.}$

$\leadsto \tt{p = \frac{ 24 - 1032 \times 2}{408}.}$

$\leadsto \tt{p = \frac{ 24 - 1032 \times \cancel 2}{ \cancel{408}}.}$

$\leadsto \tt{p = - 5.}$

Therefore, the value of p is -5.

Answer 2

Step-by-step explanation:

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HCF of 408 and 1032 is expressed as 1032 ×2+408×p Find value of p

$\huge \mathcal \orange{A} \huge \mathcal \red{n} \huge \mathcal \green{s} \huge \mathcal \blue{w} \huge \mathcal{e} \huge \mathcal \red{r - }$

At first we need to find the HCF of 408 and 1032

Let's Factorise 408 and 1032,

408 = 2 × 2 × 2 × 3 × 17

1032 = 2 × 2 × 2 × 3 × 43

= 2 × 2 × 2 × 3

= 24

HCF = 24

Now,

According to Question -

HCF of 408 and 1032 is expressed as 1032 ×2+408×p

It means,

1032 × 2 + 408 × p = 24

2064 + 408 p = 24

408 p = 24 - 2064

408 p = - 2040

$408 \: p = - 2040 \\ \\ p = \frac{ - 2040}{408} \\ \\ p = - 5$