2020 AMC 10A Problems/Problem 15
Problem
A positive integer divisor of is chosen at random. The probability that the divisor chosen is a perfect square can be expressed as , where and are relatively prime positive integers. What is ?
Solution
The prime factorization of is . This yields a total of divisors of In order to produce a perfect square divisor, there must be an even exponent for each number in the prime factorization. Note that the divisor can't have any factors of and in the prime factorization because there is only one of each in Thus, there are perfect squares. (For , you can have , , , , , or s, etc.) The probability that the divisor chosen is a perfect square is
~mshell214, edited by Rzhpamath
Video Solution
Education, The Study of Everything
~IceMatrix
~savannahsolver
Video Solution
https://youtu.be/wopflrvUN2c?t=407
~ pi_is_3.14
See Also
2020 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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