The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35, is

Given: Numbers- First = 5834
                         Second = x (Suppose)
                         And number (5834 - x) is divisible by each of 20,28,32,35
                         Let's say it is y
                         Hence 5834 - x = y
                         or x = 5834 - y
Now for x to be greatest y should be least
hence y should be least common multiple of 20,28,32,35
y = 1120
now x = 5834 - 1120
       x = 4714