What were the number of Union states in 1860?

There were 33 states in the United States in 1860. However, on December 20, 1860, South Carolina seceded from the Union, reducing the number by one at the end of the year.

Check these sites for more information.

http://en.wikipedia.org/wiki/Confederate_States_of_America#Seceding_states

http://www.netstate.com/states/tables/st_admit.htm