= 1 \cdot 60 + 45

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• السؤال: ما هو القاسم المشترك الأكبر للعددين $105$ و $165$؟
• الحل: نطبق خوارزمية إقليدس لإيجاد $\gcd(105, 165)$.
• = 1 \cdot 105 + 60
• = 1 \cdot 45 + 15
• = 3 \cdot 15 + 0
• إذن، $\gcd(105, 165) = \boxed{15}$.السؤال: أوجد مجموع جميع الزوايا $z \in [0^\circ, 360^\circ]$ التي تحقق $\sin(2z) = \frac{\sqrt{3}}{2}$.

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