Question

If d is the HCF of 45 and 27 ,find d=27x + 45y.

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Answer 1

x = 2 ; y = -1

$\underline{\mathfrak{\huge{Hence\: Solved}}}$

Answer 2

$\huge{\mathfrak{Answer}}$

x = 2 and y = -1

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$\huge{\mathfrak{Solution}}$

HCF of 45 and 27 can be calculated as:
45 = 27 × 1 + 18
27 = 18 × 1 + 9
18 = 9 × 2 + 0

Therefore, HCF = 9

ATQ,
$\sf d = 27x + 45y \\ \\ \\ \mathfrak{ From \: above \: steps \: we \: have } \\ \sf9 = 27 - 18 \times 1 \\ \sf \: \: \: = 27 - (45 - 27 \times 1) \times 1 \\ \: \: \: \sf = 27 \times 2 + 45 \times ( - 1) \\ \\ \mathfrak{Comparing \: this \: with \: given \: situation \: we \: get} \\ \sf x = 2 \: and \: y = - 1$
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