Difference between revisions of "2005 iTest Problems/Problem 4"

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[[Category: Introductory Number Theory Problems]]

Latest revision as of 19:11, 13 October 2025

Problem

How many multiples of $2005$ are factors of $(2005)^2$?

Solution 1

Taking one factor of $2005$ as a base, the other is split into $5 ^1 \cdot{ 401 ^1} = 2005$. This means $2005$ has $(1 + 1)\cdot{(1 + 1)} = 4$ divisors. Each of these divisors represents a multiple of $2005$, meaning the answer is $\boxed{4}$.

See Also

2005 iTest (Problems, Answer Key)
Preceded by:
Problem 3
Followed by:
Problem 5
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