Question

find the greatest number of four digit which on dividing 8 16 24 36 leaves remainder 4 in each case​

Answer 1

Let  x  be the unknown number. 

Then  x-10  is divisible by  16,  24,  30 and  36, according to the condition. 

It implies that  x-10  is divisible by  ,    and  . 

Hence,  x-10  is divisible by  16*5*9 = 720. 

The greatest  5-digits number divided by  720  is  99360  (it is easy to check). 

It means that  x-10 = 99360. 

Hence,  x = 99370