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If the HCF of numbers $408$ and $1032$ can be expressed in the form of $1032 x - 408 \times 5$ , then find the value of $x$ .

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0

1

2

3

answer is C.

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Detailed Solution

Given numbers are 408 and 1032.
The HCF is in the form of

1032 x - 408 \times 5

.
We need to find the value of x.

408 = 2 \times 2 \times 2 \times 3 \times 17

1032 = 2 \times 2 \times 2 \times 3 \times 43

So,
HCF

= 2 \times 2 \times 2 \times 3

\Rightarrow HCF = 24

Now, comparing the Euclid’s division algorithm i.e.,

a = bq + r

with

1032 x - 408 \times 5

,
Here,

a = 24

b = 1032

\Rightarrow 1032 x - 408 \times 5 = 24

\Rightarrow 1032 x = 2064

\Rightarrow x = 2

Therefore, the value of

x = 2

.
Hence, option 3 is correct.

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