Find the largest power of 12 that can divide 200! a. 97 b.

Is that really a simple approach? I'm not trying to be sarcastic but I still don't understand your approach.

This is how i view the problem:
200! assume - it's a big number!! obviously - you need something close to a super computer to calculate this number.
but we do know that it's even, it's greater than 12^98 (the largest answer choice) and it ends in lots of zeros (thus, it's even!).


so any number that ends with 0,2,5,4 and 8 will divide evenly into this number.

just like powers of 2 we can do the same for powers of 12

2^1=2 2^5=32 12^1=12
2^2=4 2^6=64 12^2=144
2^3=8 2^7=128 etc.
2^4=16 2^8=256

Thus use the powers of 2 as a proxy for the powers of 12 since the pattern repeats itself after the 4th power

thus the 97th power ends in 8 - thus 12^97 can divide evenly into 200! the 98th power ends in 6 so that would end in .6666667

Thus 12^97 is your answer - one of those problems that you can solve under 1.5 mins. if you see the patterns!

Nice work, Titleist.

Thanks Stoolfi. You haven't changed your avatar yet!