I need two functions one that checks if the inputed number is a prime
number and second one that splits the given number in to prafactors.

I have the first function done but the second one is a bit annoying.

The function has to take the given number and split it and save the results
in a list. Needs to split the prime number on factors and append that to an
empty list. Example:

Start with the smallest divisor, 2; see if it is a divisor and increase up to the square root + 1. So in this case
252 / 2 = 126
So 2 is a divisor. Then using 126 (divide by 2 up to square root 126 + 1)
126 / 2 = 63 -----> 2*2
Using 63
63 / 2 = False
63/3 is a divisor = 21
21 / 2 = False
21 / 3 = 7 (square root + 1 = 3)
and repeating the process yields no other divisors --> 1
You could use recursion for this, but I don't like recursion so would suggest a while loop. Come up with some code to start us off. I did a sloppy quick try using a while loop to call a function and came up with 25 lines of code.

Well?? What happend to the code? Code to, say, find the lowest divisor to start?

My quick and dirty solution, so I can delete this code.

def find_divisor(input_number):
sq = int(input_number**0.5) + 1
print("-->sq for %d = %d" % (input_number, sq))
for ctr in range(2, sq+1):
if 0 == input_number%ctr:
return ((ctr, input_number/ctr))
return((input_number, 1))
# 252 = 2*2 * 3*3 * 7*1
input_number = 252
divisors = []
found = True
while found:
## hey baby, nice pair (of numbers)
smaller_1, larger_1 = find_divisor(input_number)
print(smaller_1, larger_1)
## do again for the second (larger) number of the pair found
if smaller_1 != input_number: ## divisor found
smaller_2, larger_2 = find_divisor(larger_1)
print(" ", smaller_2, larger_2)
divisors.append((smaller_1, smaller_2))
input_number = larger_2 ## larger number of the 2nd pair
else: # no divisor=(original_number and 1)
## eliminate (1,1); a number like 6 will return (2, 3) and (1, 1)
if smaller_1 != 1:
divisors.append((smaller_1, larger_1))
found = False
print(divisors)

import random
def factors(value):
if value > 3:
for this in [2] + range(3,int(value ** 0.5)+1, 2):
if this*this > value: break
while not (value % this):
if value == this: break
value /= this
yield this
yield value
def power_factors(value):
res = list(factors(value))
return sorted((fact, res.count(fact)) for fact in set(res))
limit = 100000000
num = 10
for randval in (random.randint(1, limit) for count in range(num)):
res = ' * '.join(str(x) for x in factors(randval))
print ("factors of %i are: %s = %s" % (randval, res, power_factors(randval)))
assert eval(res) == randval
print('Factors and powers for 252: %s' % power_factors(252))

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