Difference between revisions of "2018 AMC 8 Problems/Problem 18"
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==Solution 2== | ==Solution 2== | ||
| − | Observe that | + | Observe that 69696 = 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}$. |
==See Also== | ==See Also== | ||
Revision as of 19:54, 8 November 2019
Contents
Problem 18
How many positive factors does 23,232 have?
Solution
We can first find the prime factorization of 
, which is 
. Now, we just add one to our powers and multiply. Therefore, the answer is 
Solution 2
Observe that 69696 = 264^2
\frac{1}{3}
264^2
88 \cdot 264 = 11^2 \cdot 8^2 \cdot 3 = 11^2 \cdot 2^6 \cdot 3
3 \cdot 7 \cdot 2 = 42
\boxed{\textbf{(E) }42}$.
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. 
