The product of two consecutive positive even integers is 288. What is the greater of the two integers?
So I need to find two factors of 288 that are both even and only 2 apart. One way is to start with the smallest possible even factor, which is 2, and divide 288 by 2 repeatedly until I get another even factor. Let me try that. 288 divided by 2 is 144. That's too big of a gap, so I divide by 2 again. 144 divided by 2 is 72. Still too big, so I divide by 2 again. 72 divided by 2 is 36. That's also too big, so I divide by 2 again. 36 divided by 2 is 18. That's getting closer, but still not consecutive, so I divide by 2 again. 18 divided by 2 is 9. Wait, that's not even, so I can't use it. That means I went too far with the division. So the last pair of even factors I found was 18 and 16. They multiply to 288 and they are consecutive. That must be the answer. The greater of the two integers is 18. 