2003 AMC 10A Problems/Problem 14
Problem
Let be the largest integer that is the product of exactly 3 distinct prime numbers , , and , where and are single digits. What is the sum of the digits of ?
Solution 1
Since we want to be as large as possible, we would like in to be as large as possible. So, the greatest single-digit prime. Then, cannot be because which is not prime. So . Therefore, . So, the sum of the digits of is ~ MathGenius_ (Edited by Sophia866)
Solution 2
Since is a single digit prime number, the set of possible values of is .
Since is a single digit prime number and is the units digit of the prime number , the set of possible values of is .
Using these values for and , the set of possible values of is
Out of this set, the prime values are
Therefore the possible values of are:
The largest possible value of is .
So, the sum of the digits of is
Video Solution(s)
~savannahsolver
https://www.youtube.com/watch?v=yApq-Vny_A0
~David
See Also
2003 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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