Discussion
What is the highest power of 15 that divides 80! ?
Answer: B
To find the highest power of 15 (which is \(3 \times 5\)), we need to find the highest powers of 3 and 5 in 80!. The power will be limited by the prime factor that occurs fewer times, which is 5. We count the power of 5 in 80!. Power of 5 = \(\lfloor 80/5 \rfloor + \lfloor 80/25 \rfloor = 16 + 3 = 19\). The highest power of 15 is 19.
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