In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors of 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, what would have been the remainder?

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Accepted Answer

সঠিক উত্তর: । ব্যাখ্যা: 5, 9 এবং 13 র L.C.M. $= 585$. The common difference between divisors 5, 9 and 13, and their respective remainders 4, 8 and 12 is $5-4 = 1$, $9-8 = 1$, $13-12 = 1$. So, the least number can be L.C.M of 5, 9 and 13 minus the common difference $= 585-1 = 584$. সুতরাং, বলা যায় উক্ত সংখ্যা কে 585 দ্বারা ভাগ করলে ভাগশেষ থাকবে 584.