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does the vice president live in the white house - GetMeFoodie

📅 May 1, 2026 👤 scraface

May 01, 2026

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Question: What is the sum of all the positive divisors of $ 1440 $ tha...
Solution: First, factor $ 1440 $:
= 144 \cdot 10 = (12^2) \cdot 2 \cdot 5 = (2^4 \cdot 3^2) \cdot 2 \cdo...
We seek the sum of all positive divisors $ d \mid 1440 $ such that $ d...
A divisor $ d $ satisfies $ d \equiv 1 \pmod{4} $ if it is odd (so $ d...
The odd divisors of 1440 are exactly the divisors of 45. List them:
1, 3, 5, 9, 15, 45
Now reduce each modulo 4:
$ 1 \equiv 1 \pmod{4} $
$ 3 \equiv 3 \pmod{4} $

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