Difference between revisions of "2014 AMC 12B Problems/Problem 15"
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This adds up to <math>2+8+6=16</math> powers of two which divide into our quantity, so our answer is <math>\boxed{\textbf{(C)}\ 2^{16}}</math> | This adds up to <math>2+8+6=16</math> powers of two which divide into our quantity, so our answer is <math>\boxed{\textbf{(C)}\ 2^{16}}</math> | ||
+ | ==Video Solution== | ||
+ | |||
+ | For those wanting a video: https://www.youtube.com/watch?v=iq2X86GFVBo | ||
== See also == | == See also == | ||
{{AMC12 box|year=2014|ab=B|num-b=14|num-a=16}} | {{AMC12 box|year=2014|ab=B|num-b=14|num-a=16}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 14:24, 24 September 2020
Contents
Problem
When , the number is an integer. What is the largest power of 2 that is a factor of ?
Solution
Let's write out the sum. Our sum is equal to Raising to the power of this quantity eliminates the natural logarithm, which leaves us with This product has powers of in the factor, powers of in the factor, and powers of in the factor. This adds up to powers of two which divide into our quantity, so our answer is
Video Solution
For those wanting a video: https://www.youtube.com/watch?v=iq2X86GFVBo
See also
2014 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 14 |
Followed by Problem 16 |
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 12 Problems and Solutions |
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