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No, it is impossible.
Since a binary digit has only two possible values, each digit bears less information than in decimal, where each digit can have ten different values.
There are a few numbers that are less than 19 and have more than 4 factors. The number 10 is less than 19 and has more than four factors.
If the two numbers are X and Y, it is |X - Y| + 4 or abs(X - Y) + 4
The set of natural numbers less than four is {1, 2, 3}.