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Home » Unlock Success: Powerful Social Development Examples That Prove It Works! - AssociationVoting

Unlock Success: Powerful Social Development Examples That Prove It Works! - AssociationVoting

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 لذلك، يكون حاصل الضرب قابلاً للقسمة على $8 \cdot 3 = 24$.

📌 نختبر مثالاً: $1 \cdot 2 \cdot 3 \cdot 4 = 24$، والذي ليس قابلاً للقسمة على $48$.

📌 إذن، أكبر عدد صحيح يجب أن يقسم حاصل ضرب أي أربعة أعداد صحيحة متتالية هو $\boxed{24}$.

📌 السؤال: ما هي أكبر قيمة ممكنة للقاسم المشترك الأكبر $(a,b)$، إذا كان مجموع عددين صحيحين موجبين $a + b = 96$؟

📌 الحل: ليكن $d = \gcd(a, b)$. إذن $a = dx$، $b = dy$، حيث $\gcd(x, y) = 1$.

📌 ثم $a + b = d(x + y) = 96$، لذا يجب أن يكون $d$ قاسمًا للعدد $96$.

📌 لتعظيم $d$، نختار أكبر قاسم للعدد $96$ بحيث يكون $x + y$ عددًا صحيحًا موجبًا، و$\gcd(x, y) = 1$.

📌 أكبر قاسم للعدد $96$ هو $48$، مع $x + y = 2$. الزوج $(x, y) = (1, 1)$ يحقق $\gcd(1,1)=1$.

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