A frequency divider based on a series of divide-by-2/3 cells and divide-by-1/2/3 cells using extended division range is disclosed. The frequency divider uses modified divide-by-1/2/3 cells and additional circuit elements to correctly divide an input frequency by a divisor on successive output cycles while the divisor transitions across an octave boundary. The frequency divider creates a divide-by-1 mode for unused divide-by-1/2/3 cells in the series of cells. The divide-by-1 mode passes the input clock in the unused latches of each unused divide-by-1/2/3 cell as opposed to having each unused divide-by-1/2/3 cell implement divide-by-3 mode.