Difference between revisions of "2011 UNCO Math Contest II Problems/Problem 1"
Pi3point14 (talk | contribs) (→Solution) |
Enderramsby (talk | contribs) m (→Solution) |
||
| (4 intermediate revisions by one other user not shown) | |||
| Line 5: | Line 5: | ||
== Solution == | == Solution == | ||
| − | Let <math>\ | + | Let <math>\lfloor x \rfloor</math> indicate the largest integer less than or equal to x. To solve this problem, we simply need to find the powers of 3 that go into 85!. Thus we get <math>\lfloor \frac{85}{3} \rfloor</math>. But that doesn't count the 2 powers of 3 in 9, so we need to add that to <math>\lfloor \frac{85}{9} \rfloor</math> and <math>\lfloor \frac{85}{27} \rfloor</math> and <math>\lfloor \frac{85}{81} \rfloor</math>, giving us <math>28+9+3+1=41.</math> |
== See Also == | == See Also == | ||
Latest revision as of 18:16, 5 April 2020
Problem
The largest integer 
so that 
evenly divides 
is 
. Determine the largest integer so that evenly divides 
.
Solution
Let 
indicate the largest integer less than or equal to x. To solve this problem, we simply need to find the powers of 3 that go into 85!. Thus we get 
. But that doesn't count the 2 powers of 3 in 9, so we need to add that to 
and 
and 
, giving us 
See Also
| 2011 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
