Without performing the actual division, determine the remainder when 742770349 (base ten) is divided by 2016 (base ten).

Note first that 2016/2= 1008, while 1008*625 = 630000.

Fortuitously or not, 742,770,349-201,600,000*4=-63,629,651, where both the first and second digit pairs are very close to 63*10^n. So we simply strike out the first digit pair leaving -629,651, then add back 630,000  leaving 349; but since 625 is odd so we must further add back 1,008: 349+1,008 = 1,357, which is the remainder.

 

 

Edited on July 14, 2012, 6:17 am

Posted by broll on 2012-07-13 13:24:58