Software Consultant

The idea is to take 12:00 (h = 12, m = 0) as a reference. 
Steps : 
1. Calculate the angle made by hour hand with respect to 12:00 in h hours and m minutes. 
2. Calculate the angle made by minute hand with respect to 12:00 in h hours and m minutes. 
3. The difference between the two angles is the angle between the two hands

Pseudocode :
calcAngle(h,m)
{
// validate the input
if (h <0 or m < 0 or h >12 or m > 60)
print("Wrong Input")

if (h is equal to 12) h = 0;
if (m is equal to 60)
{
m = 0;
h += 1;
if(h>12)
h = h-12;
}

// Calculate the angles moved by hour and minute hands with reference to 12:00
initialise hour_angle as 0.5 * (h * 60 + m)
initialise minute_angle as 6 * m

// Find the difference between two angles
initialise angle as absolute value of (hour_angle - minute_angle)

// Return the smaller angle of two possible angles
update angle to minimum of (360 - angle, angle)

return angle 
}

Factorial can be calculated using following recursive formula: 

n! = n * (n-1)!
n! = 1 if n = 0 or n = 1
Factorial can also be calculated iteratively as recursion can be costly for large numbers. 
Factorial(n)
{
Initialise a variable res = 1
for (i = 2 to i <= n) do :
res = res* i
return res
}