Answer:
It is 4.
Explanation:
If x is the greatest number and b the remainder the we have the equations:
ax + b = 183
cx + b = 91
dx + b = 43 where a,c and d are whole numbers.
Subtracting the last equation from the first:
ax - dx = 140
x (a - d) = 140
So x must be a factor of 140.
140 = 2 * 2 * 5 * 7
Trial and error:
Let x = 35 :
43 / 35: remainder is 8
91 / 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.