MATH SOLVE

3 months ago

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

Accepted Solution

A:

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.