Discussion
What is the highest power of 6 that divides 60! ?
Answer: A
To find the highest power of 6, we need to find the powers of its prime factors, 2 and 3, in 60!. The power will be limited by the factor that occurs fewer times. The factor 3 is less frequent than 2. So we just need to count the power of 3 in 60!. Power of 3 = \(\lfloor 60/3 \rfloor + \lfloor 60/9 \rfloor + \lfloor 60/27 \rfloor = 20 + 6 + 2 = 28\). The highest power of 6 is 28.
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