There are infinitely many prime numbers.
Proof
(from Euclid's theorem - Wikipedia)
Consider any finite list of prime numbers $p_1$, $p_2$, ..., $p_n$.
It will be shown that at least one additional prime number not in this list exists.
Let $P$ be the product of all the prime numbers in the list: $P = p_1\cdot p_2\cdot ...\cdot p_n$.
Let $q = P + 1$.
Then $q$ is either prime or not:
This means that at least one more prime number exists beyond those in the list.
This proves that for every finite list of prime numbers there is a prime number not in the list, and therefore there must be infinitely many prime numbers.
Exercise 1. Factorize number 504.
Exercise 2. Factorize number 2250.
Exercise 3. Find GCF(2250,504).
Exercise 4. Find LCM(2250,504).
Exercise 5. Determine whether 7168 is divisible by 2, 3, 4, 5, 6, 8, 9 and 10.