Question

if d is the HCF of 45 and 27 find x and y satisfying d =27x +45y

Answer 1

Hello there !

The numbers are :-
45 and 27

Lets find their HCF

BY Euclid's division Lemma :-

a = bq + r

45 = 27 x 1 + 18
27 = 18 x 1 + 9
18 = 9 x 2 + 0

HCF = d = 9

Given:-

d = 27x+45y

9 = 27x + 45y

9 = 27 - 18 x 1

18 = 45 - 27 x 1


Therefore ,
9 = 27 - [ 45 x 27 x 1 ] x 1
= 27 x 2 - 45

9 = 27 x 2 + 45 x [ -1 ]


x = 2
y = -1

Hope this Helps You !

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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