# Problems from Prime and composite numbers

Confirm which is of these numbers are prime, and which are not: $$423, 311, 505, 199$$.

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### Development:

$$423:2=21$$ (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.

### Solution:

$$311$$ and $$199$$ are prime numbers.

$$423$$ and $$505$$ are composite numbers.

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