By example:

"There are likely to be cows over that hill" - correct, many cows

"There is likely to be a herd of cows over that hill" - correct, one herd

"There are likely to be other factors" - correct, many factors

"There is likely to be a number of other factors" - correct, one collection of many factors

"There are likely to be a number of other factors" - correct, emphasizes the factors over the collection

"There are likely to be other factors" - correct if you want to treat 'other factors' as a singular group. Up for debate.

Also, "there're" is very hard to say, so using "there's" as a contraction for "there are" is, in my book, okay, even if it's not technically correct.