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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 585] and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been

24
144
292
584
Explanation:

5 | $x$         z = 13 x 1 + 12 = 25

--------------

9 | y - 4        y = 9 x z + 8 = 9 x 25 + 8 = 233

--------------

13| z - 8        $x$ = 5 x y + 4 = 5 x 233 + 4 = 1169

--------------

| 1 -12



585) 1169 (1

        585

       ----------

        584

       ----------

Therefore, on dividing the number by 585, remainder = 584.

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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 585] and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been

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