Question

Express the HCF of $468$ and $222$ as $468x+222y$, where $x$ and $y$ are integers.

Answer 1

Step 1: Calculate HCF

Prime factorization of $468$ is,

$468=2\times 2\times 3\times 3\times 13$

Prime factorization of $222$ is,

$222=2\times 3\times 37$

Hence, the HCF of $468$ and $222$ is

$2\times 3=6$

Step 2: Calculate $x$ and $y$

Now we need to express HCF of $468$ and $222$ as $468x+222y$

We can write;

. $6=222–(24\times 9)$

$\Rightarrow 6=222–\{(468–222\times 2)\times 9\}$

$\Rightarrow 6=222–(468\times 9–222\times 18)$

$\Rightarrow 6=222+(222\times 18)–(468\times 9)$

$\Rightarrow 6=222(1+18)–468\times 9$

$\Rightarrow 6=222\times 19–468\times 9$

$\Rightarrow 6=468\times (-9)+222\times \left(19\right)$

$\Rightarrow 6=468x+222y$, where $x=-9$ and $y=19$.

Hence, HCF of $468$ and $222$ can be expressed as $6=468\times (-9)+222\times \left(19\right)$.