12In dividing a no. by 585, a student employed the method of short division. He divided the no.successively by 5, 9 and 13 and got the remainders 4, 8, 12 respectively. What would havebeen the remainderif he had divided the no. by 585? Options
A) 245  B) 345  C) 560  D) 584  E) 650
Let   p   p be the number   Suppose,   p   ÷   5   =   q   p÷5=q, remainder = 4   q   ÷   9   =   r   q÷9=r, remainder = 8   r   ÷   13   =   s   r÷13=s, remainder = 12   Hence,   r   =   13   s   +   12   r=13s+12   q   =   9   r   +   8   =   9   (   13   s   +   12   )   +   8   =   117   s   +   116   q=9r+8=9(13s+12)+8=117s+116   p   =   5   q   +   4   =   5   (   117   s   +   116   )   +   4   =   585   s   +   584   p=5q+4=5(117s+116)+4=585s+584   Therefore, if   p   p is divided by 585, we will get 584 as remainder.   584
<result>D</result>
12In dividing a no. by 585, a student employed the method of short division. He divided the no.successively by 5, 9 and 13 and got the remainders 4, 8, 12 respectively. What would havebeen the remainderif he had divided the no. by 585?