Divisibility, Primes, and the Euclidean Algorithm
Section 2.2 of Computational Number Theory and Modern Cryptography by Song Y. Yan (ISBN 978-1-118-18858-3) is the oldest material in the book, and it is still the part your laptop uses. Divisibility, primes, gcd, Euclid. Yan says people have studied this for at least 3000 years. The Greeks already cared about even and odd, perfect numbers, amicable numbers, and primes. Some of those questions are still open. That is wild.