2017 AMC 8 Problems/Problem 19
Contents
Problem 19
For any positive integer , the notation denotes the product of the integers through . What is the largest integer for which is a factor of the sum ?
Solution 1
Factoring out , we have . Next, has factors of . Now has factors of , so there are a total of factors of .
Solution 2
The number of 5's in the factorization of is the same as the number fo trailing zeroes. The number of zeroes is taken by the floor value of each number divided by 5, until you can't divide by 5 anymore. Factorizing , you get . To find the number of trailing seroes in 98!, we do
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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