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Using Euclid’s division lemma, find the …

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Using Euclid’s division lemma, find the HCF of 56 and 72. If d is the HCF of 56 and 72, expressed “d” as a linear combination of 56 and 72.

Posted by Amit Shakya 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

HCF of 56 and 72

{tex}\begin{array}{l}56=8\times7=2^3\times7\\72=8\times9=2^3\times3^2\\So\;HCF(56,72)=2^3=8\end{array}{/tex}

d = 56x + 72y

⇒ 8 = 56x + 72y

Dividing by 8 both sides

1= 7x + 9y

Put x = 4 and y = –3

1 = 7 × 4 + 9(–3)

= 28 – 27

1 = 1

L.H.S = R.H.S.

Put x = –5 and y = 4

1 = 7(–5) + 9 {tex} \times {/tex} 4

= –35 + 36

1 = 1

L.H.S = R.H.S.

x = 4, and y = –3
x = –5 and y = 4
Satisfy the equations
∴ x and y are not unique.

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