Im trying to make a division in octal system $$\frac{165_{8}}{24_{8}}$$ So I have done like this using a table $$24\times 0=0_{8}$$ $$24\times 1=30_{8}$$ $$24\times 2=50_{8}$$ $$24\times 3=74_{8}$$ $$24\times 4=120_{8}$$ $$24\times 5=144_{8}$$ $$24\times 6=170_{8}$$ $$24\times 6=214_{8}$$
Next $$\frac{165_{8}}{24_{8}}=5.5_{8}$$ but this has a remainder of $0_{8}$
How must be done the fractional part, since when doing this in a calculator it solve the operation as $5.66_{8}$? How it was calculate the .66 fraction?
UPDATE I was using the wrong values on the table, it was updated. So indeed
$$\frac{165_{8}}{24_{8}}=5.66_{8}$$
The $24_8$ in the denominator is $20_{10}$. In your table you are multiplying by $24_{10}$ and then converting to base $8$. We have $5_8 \cdot 24_8=144_8$, so the remainder is $21_8$. Then $\frac {21_8}{24_8}\approx 0.663_8$