2*16!+1 is divisible by 19, so 16!+10 is divisible by 19...please explain this step

2*16! + 1 = 19k
=> 16! = (19k - 1)/2
So, 16! + 10 = (19k - 1)/2 + 10 = 9.5k + 9.5 = 9.5*(k+1)
In the first step, 2*16! is even and 2*16! + 1 is odd...So, k is odd => k+1 is even. So, let k+1 = 2t
So, 9.5*(k+1) = 9.5*2t = 19t
So, 16! + 10 = 19t => it is divisible by 19