How can I get my phone numbers to synch to my gmail contacts?

[AC Question]

I have a Galaxy S5. My contacts on my phone are supposedly synced with gmail (my phone is saying the last sync was this morning), but when I go to my gmail contacts, only a few contacts with phone numbers show up (those that are nice and tidy--where I knew the person's email before their phone number so that their phone number is linked with their email address.) Most of the contact list shows just email addresses.

I want to reset my phone because I am having a lot of problems with it, but want to make sure my phone numbers have been saved first. Anyone have any ideas?