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Structural, half-metallic, magneto-optic, and thermoelectric properties of CrTiZ (Z = As, P) half-Heusleres compounds are investigated based on density functional theory. These compounds have mechanical stability in the ferromagnetic state with a high bulk modulus. They are often half-metallic with a large and integer magnetic moment and are very attractive in spintronics, magneto-optics applications. The magnetic moments of CrTiAs and CrTiP were 2.9865 mu (B) and 3.00 mu (B), respectively, which were attributed to their ferromagnetic phase. Additionally, the positive sign of the phonon branches indicates the dynamic stability of these compounds. Applying both GGA and mBJ approximations, CrTiAs and CrTiP compounds exhibited a half-metallic nature by 100% spin polarization. The Kerr angle obtained from magneto-optic results demonstrated a high-intense peak for these compounds in the visible edge with a negative sign. Eventually, a figure of merit with a value above the room temperature was found for both compounds in which the holes are charge carriers.