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Anton

1. We know that there will definitely be enough factors of 2 in 100! in 28^k, since every even number has a factor of 2. So, we can just count the number of times that the factor of 7 appears in 100! There are 13 multiples of 7 under 100, but 49 counts for two factors, so there are a total of 14 factors of 7 in 100! So, the maximum value of k is 14.