Difference between revisions of "2014 AMC 10B Problems/Problem 12"
m (→Solution) |
(→Solution) |
||
| Line 7: | Line 7: | ||
==Solution== | ==Solution== | ||
| − | Note that <math>2,014,000,000</math> is divisible by <math>2,\ 4,\ 5,\ 8</math>. Then, the fifth largest factor would come from divisibility by <math>8</math>, or <math>251,750,000</math>, or <math>\boxed{\textbf{(C)}}</math>. | + | Note that <math>2,014,000,000</math> is divisible by <math>1,\ 2,\ 4,\ 5,\ 8</math>. Then, the fifth largest factor would come from divisibility by <math>8</math>, or <math>251,750,000</math>, or <math>\boxed{\textbf{(C)}}</math>. |
==See Also== | ==See Also== | ||
{{AMC10 box|year=2014|ab=B|num-b=11|num-a=13}} | {{AMC10 box|year=2014|ab=B|num-b=11|num-a=13}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 17:30, 16 July 2021
Problem
The largest divisor of 
is itself. What is its fifth-largest divisor?
Solution
Note that is divisible by 
. Then, the fifth largest factor would come from divisibility by 
, or 
, or 
.
See Also
| 2014 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
