Question
Show that the following pairs are co-primes: $512, 945$
✓
Answer
Given numbers are $512$ and $945.$
$\begin{array}{c|c}2&512\\\hline2&256\\\hline2&128\\\hline2&64\\\hline2&32\\\hline2&16\\\hline2&8\\\hline2&4\\\hline2&2\\\hline&1\end{array}$
$\begin{array}{c|c}3&315\\\hline3&105\\\hline5&35\\\hline7&7\\\hline&1\end{array}$
Now, $512=2\times2\times2\times2\times2\times2\times2\times2\times2=2^9$
$945=3\times3\times3\times5\times7=3^3\times5\times7$
Thus, the $HCF$ of $512$ and $945$ is $1.$
$\therefore 512$ and $945$ are co-primes.
$\begin{array}{c|c}2&512\\\hline2&256\\\hline2&128\\\hline2&64\\\hline2&32\\\hline2&16\\\hline2&8\\\hline2&4\\\hline2&2\\\hline&1\end{array}$
$\begin{array}{c|c}3&315\\\hline3&105\\\hline5&35\\\hline7&7\\\hline&1\end{array}$
Now, $512=2\times2\times2\times2\times2\times2\times2\times2\times2=2^9$
$945=3\times3\times3\times5\times7=3^3\times5\times7$
Thus, the $HCF$ of $512$ and $945$ is $1.$
$\therefore 512$ and $945$ are co-primes.
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