Well, ... Here's my answer: 389.2 (to be exact 389.173809 ) times.

1) you need to know the semi-major axis of the Moon's orbit (or radius). This is documented as: 384399 km (0.00257 AU). Let's call it rM. The diameter of the moon's orbit is just the radius times 2 or 2(rM) or 768,798 km. We'll the diameter of the Moon's orbit dM.

2) Then you need to do the same for Earth's Orbit around the sun. The Semi-major axis of Earth's orbit is: 149,598,023 km (92,955,902 mi) (1.000001018 AU). let's call it rE. The diameter of the Earth's orbit is just the radius times 2 or 2(rE) or 299,196,046 km. We'll call the diameter of Earth's orbit: dE

3) Now just divide dM into dE and you have your answer.

dE / dM = 299,196,046 km / 768,798 km = 389.173809 times (the km's cancel each other out)