It’s not only the Sieve of Eratosthenes that uses the speed advantage of iterating over multiples.
Number of Divisors of Each Integer up to $n$
Storing Divisors
Even Faster Factorization by Storing Prime Divisors $(\mathcal{O}(\log n))$
These are some of the algorithms worth mentioning. There are so many other similar algorithms that use the same idea, but no doubt you can implement them yourselves!