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Home » \( 5^3 = 125 \equiv 5 \) - Ready Digital AB

\( 5^3 = 125 \equiv 5 \) - Ready Digital AB

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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📌 Total area = \(6 \times 9\sqrt{3} = 54\sqrt{3}\) cm².

📌 #### \(54\sqrt{3}\) cm²**Question:

📌 A philosopher of science is contemplating the symmetry of natural laws and wonders: If the sum of two positive integers \(a\) and \(b\) equals 2023, what is the largest possible value of \(\gcd(a, b)\)?

📌 To maximize \(\gcd(a, b)\), we note that if \(\gcd(a, b) = d\), then \(a = dx\) and \(b = dy\) for some integers \(x\) and \(y\) with \(\gcd(x, y) = 1\). Thus, \(a + b = dx + dy = d(x + y) = 2023\). Therefore, \(d\) must divide 2023.

📌 First, we factor 2023 to find its divisors. Checking small prime numbers:

📌 2023 is odd, so not divisible by 2.

📌 Sum of digits of 2023 is \(2+0+2+3 = 7\), not divisible by 3.

📌 2023 does not end in 0 or 5, so not divisible by 5.

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