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Home » The greatest common divisor is \(\boxed31\). - Nurtured Nest

The greatest common divisor is \(\boxed31\). - Nurtured Nest

📅 May 8, 2026 👤 scraface

May 08, 2026

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📌 Solution: Let the number of participants from the first neighborhood be $ 4x $ and from the second be $ 9x $. The total number of participants is:

📌 The number of participants from the second neighborhood is:

📌 Question: How many positive 4-digit numbers are divisible by both 3 and 4?

📌 Solution: A number divisible by both 3 and 4 must be divisible by their least common multiple:

📌 We now find how many 4-digit numbers are divisible by 12.

📌 The number of multiples of 12 from 1008 to 9996 is:

📌 Solution: A regular hexagon inscribed in a circle has side length equal to the radius $ r $. The area $ A $ of a regular hexagon with side length $ s $ is given by:

📌 Initially, $ s = r $, so the original area is:

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