So the answer has to be 21/26/31/36... etc.
If he had to then divide into groups of 4 he'd have left over: 1, 0, 3, 0...
If ditto 3, ditto: 0, 2... bang there it is - 26
If six, same as three... 26
If seven... nope
eight, same as four
So I worked it out even though the question was missing. Pretty Awesome, beat that Hawkings.
My answer is "Yes", because when a unit of something is "taken away" from a set, it would be a whole number for whichever set to which it was added, and after all, negative numbers perform the practical function of removing just as positive numbers perform the function of adding and aggregating; and one mustn't lose sight of the practical origin of maths.
However, factoring in the pedantic nature of humans for trying to look clever through verbal technicalities, If you define a whole number in a particular way, then whether it is one will be a tautology based entirely on your prior definition. What you are really asking for is the definition of a whole number, rather than whether a negative number is a whole number. When you think about it deeply, there is no such thing as a whole number, anymore than there was born a man without parents who didn't eat, age or breathe. There is just 'stuff'.