Question

. If the HCF of 5768 and 4635 is expressible in the form 5768x – 4635y, then find one pair of values of x and y

Answer 1

$\begin{array}{r|l}&1\\\cline{2-2}4635&5768\\&4635\\\cline{2-2}&1133\end{array}$

$\begin{array}{r|l}&4\\\cline{2-2}1133&4635\\&4532\\\cline{2-2}&103\end{array}$

$\begin{array}{r|l}&11\\\cline{2-2}103&1133\\&1133\\\cline{2-2}&0\end{array}$

$\text{From the last division, it is clear that 103 is the HCF of 5768 and 4635}$

$\text{Also, by division algorithm }$

$5768=1(4635)+1133$

$5768-1(4635)=1133$......(1)

$4635=4(1133)+103$......(2)

$\text{Using (1) in (2), we get}$

$4635=4(5768-1(4635))+103$

$4635=4(5768)-4(4635)+103$

$\implies\;103=-4(5768)+5(4635)$

$\implies\bf\;103=(-4)(5768)-(-5)(4635)$

$\therefore\textbf{One pair of x and y is (-4,-5)}$

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