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

• A. $24$
• B. $144$
• C. $292$
• D. $584$

Answer 1

The correct option is D $584$

$5lx$ $z=13x1+12=25$
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$9ly-4$ $y=9xz+8=9x25+8=233$
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$13lz-8$ $x=5xy+4=5x233+4=1169$
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$l1-12$
Therefore, on dividing the number by $585$, remainder $=584$