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The remainder of the division, by 4, is a number between 0 and 3. In the case of binary, this would maintain the last two bits of the original number.
28-bits
The largest binary number that can be expressed with 16 bits is 1111111111111111, which is equivalent to 65,535 in decimal. This number uses all 16 bits set to 1. In general, for an n-bit binary number, the maximum value is (2^n - 1). Thus, for 16 bits, it is (2^{16} - 1 = 65,535).
As quoted from Google Books, "Word size refers to the number of bits that a microprocessor can manipulate at one time."
A nibble consists of 4 bits. The binary number "1011 1101 1001 1110" contains 16 bits in total. Therefore, to find the number of nibbles, you divide the total number of bits by 4, which results in 4 nibbles.