Using Euclid’s division lemma, find the …
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Sia ? 4 years, 10 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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