You might say to yourself, "Well, that's easy, just divide every number up to 624 into 625, and for each number that you don't get a remainder, that number is a factor of 625."
If that was how you proposed to solve the problem, you would be taking the approach of a brute force algorithm. First you would divide 625 by 2 and see if it comes out evenly, then divide it by 3, then 4, and so forth. After you had tried every possible divisor, you certainly would know which ones divided 625 evenly. Along the way, however, you might notice that there might be a faster way to do it.
Can you think of a more efficient algorithm than that?
A more efficient algorithm might be more complicated to describe, but when you actually perform all of the steps it will take less time and effort.