If the integer N leaves a remainder of 1234 when divided by 2013, what is the remainder when N is divided by 183?

Answer 1

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