Q: i was looking for the prime factorization of 1945 in my head and i'm just doing it naively. took 5 out so i was at 389*5, but then i checked everything up to 41 before going "yeah maybe 389 is prime" and calling it a day, but idk really. is there a quick way to make sure?
A: you don't have to go any further than the square root. for example, you actually didn't have to check any higher than 23 because 23 squared is in the 500s which is already higher than 389. this technique works as long as you checked everything below it and didn't make any mistakes