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?
Explanation: 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.
