Prime and composite numbers

$423:2=21$ (and remainder $3$).

$423:3=141$ (and remainder $0$). It is an exact division, which means that $3$ is a divisor of $423$. Therefore, $423$ is not a prime number. $$\\\\$$

$311:2=155$ (and remainder $1$).

$311:3=103$ (and remainder $2$).

$311:5=62$ (and remainder $1$).

$311:7=44$ (and remainder $3$).

$311:9=34$ (and remainder $5$).

$311:11=28$ (and remainder $3$).

$311:13=23$ (and remainder $12$).

$311:17=18$ (and remainder $5$).

$311:19=16$ (and remainder $7$). In this division, the divisor is greater than the quotient, therefore we can stop doing divisions. $311$ is a prime number. $$\\\\$$

$505:2=252$ (and remainder $1$).

$505:3=167$ (and remainder $2$).

$505:5=101$ (and remainder $0$). It is an exact division. Therefore $505$ is not a prime number. $$\\\\$$

$199:2=99$ (and remainder $1$).

$199:3=66$ (and remainder $1$).

$199:5=39$ (and remainder $4$).

$199:7=28$ (and remainder $3$).

$199:9=22$ (and remainder $1$).

$199:11=18$ (and remainder $1$).

$199:13=15$ (and remainder $4$).

$199:17=11$ (and remainder $12$). In this division, the divisor is greater than the quotient, so we can stop doing divisions. $199$ is a prime number.