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Omni-MATH / Let N be a three-digit integer such that the difference between any two positive integer factors of N is divisible by 3 . Let d(N) denote the number of positive integers which divi…

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problem

Let NN be a three-digit integer such that the difference between any two positive integer factors of NN is divisible by 3 . Let d(N)d(N) denote the number of positive integers which divide NN. Find the maximum possible value of N⋅d(N)N \cdot d(N).
Plain-text mathematical notation (without MathML)
Let N be a three-digit integer such that the difference between any two positive integer factors of N is divisible by 3 . Let d(N) denote the number of positive integers which divide N. Find the maximum possible value of N⋅d(N).
Original LaTeX notation
Let $N$ be a three-digit integer such that the difference between any two positive integer factors of $N$ is divisible by 3 . Let $d(N)$ denote the number of positive integers which divide $N$. Find the maximum possible value of $N \cdot d(N)$.

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Source and history

task_id
eaa955bf-36a1-5933-9be7-06aee8594503
task_key
test--eaa955bf-36a1-5933-9be7-06aee8594503
task_revision_id
1
config / split
/ test

Official source

initial import