Question

When the HCF of $468$ and $222$ is written in the form of $468x+222y$ then the value of $x$ and $y$ is

• A. $x=-9andy=19$
• B. $x=9andy=-19$
• C. $x=9andy=19$
• D. $x=-9andy=-19$

Answer 1

The correct option is A $x=-9andy=19$

According to the definition of Euclid's theorem,

$a=b\times q+r$ where $0\le r<b.$

HCF of $468$ and $222$
$468=(222\times 2)+24$
$222=(24\times 9)+6$
$24=(6\times 4)+0$
$\therefore HCF=6$

$6=222-(24\times 9)$

$=222-[(468-222\times 2)\times 9]$ [where $468=222\times 2+24$]

$=222-[468\times 9-222\times 2\times 9]$
$=222-(468\times 9)-(222\times 18)$
$=222+(222\times 18)-(468\times 9)$
$=222[1+18]-468\times 9$
$=222\times 19-468\times 9$
$=468\times -9+222\times 19$
$\therefore x=-9$ and $y=19$.