SOLUTION: What is the largest positive integer k so that 5k divides 26!?

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Question 255259: What is the largest positive integer k so that 5k divides 26!?

Found 2 solutions by drk, jsmallt9:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Part of 26! are the numbers: 5, 10, 15, 20, and 25.
5*1 = 5
5*2 = 10
5*3 = 15
5*4 = 20
5*5 = 25
factor out the 5's from the left and we have
5(1*2*3*4*5)
or 5*120.
So, k = 120

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If k is an integer, then 5k would be a multiple of 5. Only numbers that end in 5 or 0 can be divided evenly by a multiple of 5. So 5k will not divide into 26 (or 261) evenly if k is an integer. Therefore there is no solution unless you made a mistake when posting the question.