A student used the method of short division and divided the number successively by 5, 9 and 13 and got the remainders 4, 8 and 12, respectively. If he had divided the number by 585, the remainder would have been ___________.

Let the unknown number be N. Successive division by 5, 9 and 13 with remainders of 4, 8 and 12 means N equals 5 times 9 times 13 times k plus 12 times 45 plus 8 times 5 plus 4. Calculate the constant part to get 585k plus 540 plus 40 plus 4, which simplifies to 585k plus 584. Because 584 is less than the divisor 585, the remainder is 584.

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