Amount spent in dollars = 13.69

Therefore: Amount spent in cents = 13.69*100 = 1369

Now

(Number of friends sharing the bill)*(Amount shared by each) = 1369

In the above eqn both nos of friends sharing the bill and amount shared by each must be whole numbers as people cannot be in fractions, and cent being the smallest coin available, amount in denominations smaller than a cent cannot be shared equally.

It so happens that there are only two factors of 1369. These are 37 and 37, or

1369 = 37*37

1369 is not divisible by any other whole number.

Therefore the number of friends has to be 37, and share of bill of each has to be 37 cents.