Question

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 and 12 If he had divided number by 585 then find out the remainder

Answer 1

5 | x z = 13 x 1 + 12 = 25
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9 | y - 4 y = 9 x z + 8 = 9 x 25 + 8 = 233
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13| z - 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169
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| 1 -12

585) 1169 (1
585
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584
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$\therefore ondividingthenumberby585,remainder=584$.