  We present results from the first solar full-disk F$_{10.7}$ (the radio flux
at $10.7$ cm, $2.8$ GHz) image taken with the S-band receivers on the recently
upgraded Karl G. Jansky Very Large Array (VLA) in order to assess the
relationship between the F$_{10.7}$ index and solar extreme ultra-violet (EUV)
emission. To identify the sources of the observed $2.8$ GHz emission, we
calculate differential emission measures (DEMs) from EUV images collected by
the Atmospheric Imaging Assembly (AIA) and use them to predict the
bremsstrahlung component of the radio emission. By comparing the bremsstrahlung
prediction and radio observation we find that $8.1\pm 0.5\%$ of the variable
component of the F$_{10.7}$ flux is associated with the gyroresonance emission
mechanism. Additionally, we identify optical depth effects on the radio limb
which may complicate the use of F$_{10.7}$ time series as an EUV proxy. Our
analysis is consistent with a coronal iron abundance that is $4$ times the
photospheric level.
