Difference between revisions of "2014 AMC 10B Problems/Problem 12"

(Problem)
(Solution)
Line 6: Line 6:
  
 
==Solution==
 
==Solution==
 +
 +
Note that <math>2014000000</math> is divisible by <math>2,\ 4,\ 5,\ 8</math>. Then, the fifth largest factor would come from divisibility by 8, or <math>251750000</math>, or <math>\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 13:19, 20 February 2014

Problem

The largest divisor of $2,014,000,000$ is itself. What is the fifth-largest divisor?

$\textbf {(A) } 125, 875, 000 \qquad \textbf {(B) } 201, 400, 000 \qquad \textbf {(C) } 251, 750, 000 \qquad \textbf {(D) } 402, 800, 000 \qquad \textbf {(E) } 503, 500, 000$

Solution

Note that $2014000000$ is divisible by $2,\ 4,\ 5,\ 8$. Then, the fifth largest factor would come from divisibility by 8, or $251750000$, or $\textbf{(C)}$.

See Also

2014 AMC 10B (ProblemsAnswer KeyResources)
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. AMC logo.png