2018 AMC 8 Problems/Problem 18
Contents
Problem
How many positive factors does have?
Solution 1
We can first find the prime factorization of , which is . Now, we 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 to use 3 and 11 divisibility rules to observe that .
Another way is to spot the "32" and compute that .
Solution 2 (Using 264^2)
Observe that = , so this is of which is , which has factors. The answer is .
Video Solution
~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 | |
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All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.