2013 AMC 12B Problems/Problem 9
Problem
What is the sum of the exponents of the prime factors of the square root of the largest perfect square that divides ?
Solution
Looking at the prime numbers under , we see that there are factors of , factors of , and factors of . All greater primes are represented once or none in , so they cannot be part of the square. Since we are looking for a perfect square, the exponents on its prime factors must be even, so we can only use of the factors of . Therefore, the prime factorization of the square is . To find the square root of this, we halve the exponents, leaving . The sum of the exponents is
Video Solution by OmegaLearn
https://youtu.be/ZhAZ1oPe5Ds?t=2694
~ pi_is_3.14
Video Solution
~someone
See also
2013 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
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All AMC 12 Problems and Solutions |
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