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Home » Fast, Fierce, and FULL of Flavor—What’s In N Out Sauce Will Blow Your Mind! - Dachbleche24

Fast, Fierce, and FULL of Flavor—What’s In N Out Sauce Will Blow Your Mind! - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Hence, the greatest common divisor is \(oxed{3}\).

📌 A community nutrition educator is organizing a cooking workshop. If the number of participants on two consecutive days are \( p \) and \( q \), and it is known that \( p + q = 150 \), what is the greatest possible value of \(\gcd(p, q)\)?

📌 Let \( d = \gcd(p, q) \). Then \( p = dk \), \( q = dl \) with \(\gcd(k, l) = 1\), and:

📌 dk + dl = 150 \implies d(k + l) = 150

📌 To maximize \( d \), minimize \( k + l \). Since \(\gcd(k, l) = 1\), the smallest sum is 2 (when \( k = 1 \), \( l = 1 \)). Then:

📌 d imes 2 = 150 \implies d = 75

📌 Since 75 divides 150 and \( k + l = 2 \) satisfies coprimality, the largest possible \(\gcd(p, q)\) is \(oxed{75}\).

📌 An entomologist is examining the cycles of a rare insect species, where the cycle length is represented by a three-digit integer \( z \) such that \( z \) is divisible by 7, 11, and 13. What is the smallest such \( z \)?

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