If M is the product of all positive integers greater than 59 and less than 71, then what is the greatest integer n for which M/(6^n) is an integer?
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This one took me a while. I kept counting 6s and then realized I need to break 6 into its prime factors first.
Same here! Took me a minute to realize I need to count 2s and 3s and then use the limiting one.
Wait why is the range 60 to 70 and not 60 to 69? "greater than 59 and less than 71" means 60 through 70 right?
yes! 60 to 70 inclusive. I almost dropped 70 too lol
got 7 first because I just counted multiples of 6. then reread and felt silly. classic trap.
medium-hard for me. the concept is easy but tracking all the prime factors of 60-70 without missing any is where I slip. got there eventually though
What it tests
Your command of divisibility, primes, factors, parity, and how the GMAT tests properties of integers.
Common trap
Forgetting that 1 is not prime, that 0 is divisible by every integer, or that negative numbers flip your assumptions.