What number goes in to 209 apart from 1 and 209?

Answer 1

209/11 = 19

In testing to see whether an integer is prime, the only candidates against which one needs to test the number are less than or equal to its square root.

Simple rules here allow us to exclude 2 (and hence 4, 6, 8, 10, 12, and 14), 3 (and hence 6, 9, and 12), and 5 (and hence 10). You might or might not know the quick test for divisibility by 7, by 11 (it's cute), or by 13, but at most you'd have to try dividing 209 by those three numbers.