A three-digit positive integer n has the property that when 2024 is divided by n, the remainderis 4. What is the sum of all such three-digit positive integers n?
Question
A three-digit positive integer n has the property that when 2024 is divided by n, the remainderis 4. What is the sum of all such three-digit positive integers n?
Solution
To solve this problem, we need to understand that if a number n divides 2024 with a remainder of 4, then n must be a factor of 2020 (2024 - 4).
Step 1: Find the factors of 2020.
The factors of 2020 are: 1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010, 2020.
Step 2: Identify the three-digit factors.
The three-digit factors of 2020 are: 101, 202, 404, 505, 1010.
Step 3: Sum the three-digit factors.
101 + 202 + 404 + 505 + 1010 = 2222.
So, the sum of all such three-digit positive integers n is 2222.
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