A frequency divider circuit uses a base counter to frequency divide a clock signal with period T by an integer value N and employs a cyclic rotational select circuit to select among multiple equally phase shifted signals of a multiple phase clock to generate a fractional term P/k where P is variable from 0 to k−1. The counter counts an output clock that corresponds to the output of a multiplexer selecting from among the multiple clock phases. Depending on the desired fractional term, after N counts of the output clock phases of the multiple phase clock are selected glitch free by rotationally selecting a first phase, and skipping either 0, 1, 2 . . . up to k−1 sequential phases to generate fractional terms 0, 1/k, 2/k, 3/k . . . k−1/k, respectively, thus providing frequency division corresponding to N+P/k where P may be varied from 0 to k−1.