Difference between revisions of "2018 AMC 8 Problems/Problem 18"
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Observe (how??) that <math>69696</math> = <math>264^2</math>, so this is <math>\frac{1}{3}</math> of <math>264^2</math> which is <math>88 \cdot 264 = 11^2 \cdot 8^2 \cdot 3 = 11^2 \cdot 2^6 \cdot 3</math>, which has <math>3 \cdot 7 \cdot 2 = 42</math> factors. The answer is <math>\boxed{\textbf{(E) }42}</math>. | Observe (how??) that <math>69696</math> = <math>264^2</math>, so this is <math>\frac{1}{3}</math> of <math>264^2</math> which is <math>88 \cdot 264 = 11^2 \cdot 8^2 \cdot 3 = 11^2 \cdot 2^6 \cdot 3</math>, which has <math>3 \cdot 7 \cdot 2 = 42</math> factors. The answer is <math>\boxed{\textbf{(E) }42}</math>. | ||
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+ | ==Video Solution (CREATIVE ANALYSIS!!!)== | ||
+ | https://youtu.be/44kIAfS5iJk | ||
+ | |||
+ | ~Education, the Study of Everything | ||
==Video Solution by OmegaLearn== | ==Video Solution by OmegaLearn== |
Revision as of 14:16, 30 March 2023
Contents
Problem
How many positive factors does 23,232 have?
Solution 1
We can first find the prime factorization of , which is
. Now, we just add one to our powers and multiply. Therefore, the answer is
Note:
23232 is a large number, so we can look for shortcuts to factor it.
One way to factor it quickly is use 3 and 11 divisibility rules to observe that .
Another way is to spot the "32" and compute that .
Solution 2
Observe (how??) that =
, so this is
of
which is
, which has
factors. The answer is
.
Video Solution (CREATIVE ANALYSIS!!!)
~Education, the Study of Everything
Video Solution by OmegaLearn
https://youtu.be/6xNkyDgIhEE?t=1515
~ pi_is_3.14
Video Solution
~savannahsolver
See Also
2018 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.