I have a 2013 f150 with hid what is the closest color bulb to the factory hid, the fogs look yellow.

 

You have the oem projectors? Nearly impossible to match them unless if you get some custom retrofit fogs. Stock oem projectors are 4300k I swapped mine out with 6k bulbs and put some 3k hids on my fogs.

 

Swapped my fogs for some 5k LED's from vleds.com You will need the H10 style and it will swap right in. Took five minutes to swap both, and I was taking my time. Looks awesome now. I use them as daytime running lights during the day.