Find the greatest number that will divide 43,91,183 so as to leave the same remainder in each case

Answer:It is 4.Step-by-step explanation:If x is the greatest number  and b  the remainder the we have the equations:ax + b = 183cx + b = 91dx + b = 43    where a,c and d are whole  numbers.Subtracting  the last equation from the first:ax - dx = 140x (a - d) = 140So x must be a factor of 140. 140 = 2 * 2 * 5 * 7Trial and error:Let  x = 35 :43 / 35: remainder  is 891 / 35 : rem = 21    So NOT 35.x = 7:  43/7 rem = 1            91 / 7 rem = 0  So NOT 7.x = 5:  43/5  rem = 3, 91/5 rem = 1 ,  NOT 5.x = 10  43/10 rem 3, 91/10 rem 1 NOT 10.x = 20  43/20 rem 3, 91/20 rem 11 so NOT 20.x = 28 43/28 rem 15, 91/28 rem 7 so NOT 28.x = 14: 43 / 14  rem =1,  91/14 rem =  7  NOT 14.x = 4:   43/4 rem 3, 91/4 rem 3, 183 / 4 rem 3. So it is 4.