Difference between revisions of "2014 AMC 10B Problems/Problem 12"
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==Problem== | ==Problem== | ||
− | The largest divisor of <math>2,014,000,000</math> is itself. What is | + | The largest divisor of <math>2,014,000,000</math> is itself. What is its fifth-largest divisor? |
<math> \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 </math> | <math> \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 </math> | ||
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==Solution== | ==Solution== | ||
− | Note that <math>2 | + | 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}} |
Latest revision as of 18:30, 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 | |
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All AMC 10 Problems and Solutions |
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