We study a Zeeman slower using the magnetic field generated by a pair of coils for a magneto-optical trap. The efficiency of the Zeeman slower is shown to be dependent on the intensity and frequency detuning of the laser light for slowing the atoms. With the help of numerical analysis, optimal experimental parameters are explored. Experimentally, the optimal frequency detuning and intensity of the slowing beam are explored, and 4 × 10⁷ ytterbium atoms are trapped in the magneto-optical trap.