Pipelined architecture for secret key block ciphers
the number of stages must be a divisor of number of rounds

That applies to pipelined and to iterative implementations where one stage implements $k\ge2$ rounds out of $K$, and we want each of the $K/k$ stages needed for a full block cipher strictly identical. That requirement could be waived by making less rounds in the last stage, or in an iterative implementation using an extra multiplexer extracting the output after $K\bmod k$ rounds in the last of the $\lceil K/k \rceil$ stages. That requirement does not apply at all to implementation with a single round, or less, per pipeline stage.

in AES, since there is 4 operations inside every round then it is possible to make 4 stages?

Yes, with 4 stages per round, thus $4K$ stages per block ($K\in\{10,12,14\}$ depending on key size). That's useful in an iterative implementation (which goal is reduced silicon area at the expense of throughput). One stage still needs to perform 4 identical byte substitutions (since each 16 bytes of a block go through that at each round) in the SubBytes steps, thus a minimum-area implementation might further subdivide that, for a total of $16K$ steps per block.

but what about the last round?

Indeed the last round needs to be special-cased; in a pipeline that's different (simpler) function in the last round, in an iterative implementation that's an extra input to the logic to inhibit MixColumns, held to a different state during the last of the $K$ rounds.