Math Warm Up #1

I'd like to post occasional 'Problems of the Day' that I've written and shared with colleagues. Pls pls share your favorites too (but leave answers and solutions to be kind!).

Here's one for today, appropriate for grades 7-12:

Let N$ denote the largest odd positive integer factor of the positive integer N.
For example, 6$ = 3, 7$ = 7 and 8$ = 1.
If N < 100, what is the largest value of N for which N$ = 3.
No calculator allowed!

and the answer is...
I'll post it around noon today (yup, that's hypocritical of me) but I know you'll have it solved way before then! BTW, the math skills and concepts needed are middle school but most students struggle with the notation (hence the name of my blog!) and the meanings of key terms like factor. There's also a lot of verbiage embedded in just a few words. Have fun!

Ok, here it is: 96
Comments: Many students who attempt this question (some will simply give up and say, "I don't understand it"), will come up with 99 since 99 is divisible by 3. However, the largest odd factor of 99 is 99, not 3! This suggests we need an even number divisible by 3. The next candidate going down by 3's is 96 = 32 x 3. All factors of 96 will be even except for 1 and 3. Seems like such an easy problem, right? Way too easy for high schoolers? Try it and comment on the results and the grade level tomorrow!