We present the first census of giant molecular clouds (GMCs) complete down to 10$^6 M_{odot}$ and within the inner 4 kpc of the nearest giant elliptical and powerful radio galaxy, Centaurus A. We identified 689 GMCs using CO(1--0) data with 1 spatial resolution ($sim 20$ pc) and 2 km/s velocity resolution obtained with the Atacama Large Millimeter/submillimeter Array (ALMA). The $I$(CO)-$N$(H$_2$) conversion factor based on the virial method is $X_{rm CO}$ = $(2 pm 1 )times10^{20}$ cm$^{-2}$(K km/s)$^{-1}$ for the entire molecular disk, consistent with that of the disks of spiral galaxies including the Milky Way, and $X_{rm CO}$ = $(5 pm 2)times10^{20}$ cm$^{-2}$(K km/s)$^{-1}$ for the circumnuclear disk (CND, within a galactocentric radius of 200 pc). We obtained the GMC mass spectrum distribution and find that the best-truncated power-law fit for the whole molecular disk, with index $gamma simeq -2.41 pm 0.02$ and upper cutoff mass $sim 1.3 times 10^{7} M_{odot}$, is also in agreement with that of nearby disk galaxies. A trend is found in the mass spectrum index from steep to shallow as we move to inner radii. Although the GMCs are in an elliptical galaxy, the general GMC properties in the molecular disk are as in spiral galaxies. However, in the CND, large offsets in the line-width-size scaling relations ($sim$ 0.3 dex higher than those in the GMCs in the molecular disk), a different $X_{rm CO}$ factor, and the shallowest GMC mass distribution shape ($gamma = -1.1 pm 0.2$) all suggest that there the GMCs are most strongly affected by the presence of the AGN and/or shear motions.
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