One way with base R:

df = data.frame(Count = c(1, 2, 3, 4, 5))
# Use the modulo operator to return the remainder of dividing by 2
df$evenodd <- df$Count %% 2
# Relabel 0 = Even, 1 = Odd
df[df$evenodd == 0,]$evenodd = "Even"
df[df$evenodd == 1,]$evenodd = "Odd"