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Home » The sum of the distinct prime factors is \(\boxed10\). - Leaselab

The sum of the distinct prime factors is \(\boxed10\). - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 + (n-1) \cdot 7 \leq 200 \Rightarrow (n-1) \cdot 7 \leq 197 \Rightarrow n-1 \leq 28.14 \Rightarrow n \leq 29

📌 Thus, there are 29 such numbers.

📌 Question: A community garden coordinator in Brooklyn is planning a layout where plots are labeled in base 7. If a plot is labeled $ 314_7 $, what is its label in base 10?

📌 Solution: Convert $ 314_7 $ to base 10:

📌 314_7 = 3 \cdot 7^2 + 1 \cdot 7^1 + 4 \cdot 7^0 = 3 \cdot 49 + 1 \cdot 7 + 4 = 147 + 7 + 4 = 158

📌 \boxed{158}

📌 Question: What is the remainder when $ 2023 + 2025 + 2027 + 2029 $ is divided by 8?

📌 + 2025 + 2027 + 2029 = (2023 + 2029) + (2025 + 2027) = 4052 + 4052 = 8104

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