We study conformal higher spin (CHS) fields on constant curvature backgrounds. By employing parent formulation technique in combination with tractor description of GJMS operators we find a manifestly factorized form of the CHS wave operators for symmetric fields of arbitrary integer spin $s$ and gauge invariance of arbitrary order $tleq s$. In the case of the usual Fradkin-Tseytlin fields $t=1$ this gives a systematic derivation of the factorization formulas known in the literature while for $t>1$ the explicit formulas were not known. We also relate the gauge invariance of the CHS fields to the partially-fixed gauge invariance of the factors and show that the factors can be identified with (partially gauge-fixed) wave operators for (partially)-massless or special massive fields. As a byproduct, we establish a detailed relationship with the tractor approach and, in particular, derive the tractor form of the CHS equations and gauge symmetries.
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