find the greatest number that will divide 185 and 300 leaving remainders 3 and 6 respectively.

On dividing 185, the remainder is 3, this means the number divides 185-3=182 exactly

 

Similarly, on dividing 300, the remainder is 6, meaning the number divides 300-6=294 exactly

 

So the number divided both 182 and 294 exacly

 

Factors of 182 are 182=2x7x13

Factors of 294 are 294=2x3x7x7

 

So the greatest common factor is 2x7=14

 

Hence the greatest number of such sort is 14.