2007 Cyprus MO/Lyceum/Problem 28
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Problem
The product of 
is an integer number whose last digits are zeros. How many zeros are there?
Solution
The number of zeros at the end of a number is determined by the number of 2's and 5's in its prime factorization.
There are 12 
's and 19 
's. Each pair adds a zero, but any extras don't count (in this case, the 7 extra 's).
See also
| 2007 Cyprus MO, Lyceum (Problems) | ||
| Preceded by Problem 27 | Followed by Problem 29 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
