2021 Fall AMC 10B Problems/Problem 6
Contents
[hide]Problem
The least positive integer with exactly distinct positive divisors can be written in the form , where and are integers and is not a divisor of . What is
Solution
Let this positive integer be written as . The number of factors of this number is therefore , and this must equal 2021. The prime factorization of 2021 is , so and . To minimize this integer, we set and . Then this integer is . Now and so
~KingRavi
Solution 2
See Also
2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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