#Prime numbers < 100
primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]
factors = [0]*VMAX #Prime factors
repeat = [0]*VMAX #Store times each factor repeats
i = 0
n = 0
k = 0
spacer = 0
a = raw_input("Type a number to find it's prime factors:")

#Start to divide the number by prime numbers while a is not 1
for i in range(VMAX):

while ((a != 1) & (int (a) % primes[i] == 0)):

a = int (a) / primes[i]

factors[i] = primes[i] # The prime factor is the one being used

n = n + 1 #*Count how many times each prime is used

# formatting
if(spacer == 0):
print
spacer = spacer + 1
else:
if(n == 1):
print
print
print primes[i],
print n,
print " ",

if (int (a) % primes[i] == 0):
n = 0 #Reinitialize counter
repeat[k] = n

n = 0
k = k + 1
print
print
print "Prime factors:"

#Print all factors in the array != 0
for i in range(VMAX):

if (factors[i] !=0):
#Since x ^ 0 = 1, we have to print x ^ 1 instead
if (repeat[i] == 0):
print factors[i],
else: print "%s ^ %s " % (factors[i], repeat[i]),