If the integer N leaves a remainder of 1234 when divided by 2013, what is the remainder when N is divided by 183?
The number N can be written in the format :
Dividend = Divisor * Quotient + Remainder as
N = 2013 * Q + 1234
This can be written as
N = 183 * 11 * Q + 1234
Dividing both sides by 183 , we get
N/183 = 11 * Q + 1234/183
N/183 = 11 * Q + (1098 +136)/183
N/183 = 11 * Q + 6 + 136/183
Multiplying both sides by 183 , we get
N = 183 * ( 11* Q + 6 ) + 136
If 11* Q + 6 = K
N = 183 * K + 136
which means 136 is the remainder when N is divided by 183