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import PIL, math
import numpy as np
#Problem 3 Largest Prime Factor
###INEFFICIENT METHODS###
#def isPrime(number):
# if (number <=1):
# return False
# for i in range(2,number):
# if(number%i==0):
# return False
# return True
#def prime_factors(number):
#primes = []
#for i in range(number, 2, -1):
#if(number%i==0):
#if (isPrime(i)):
#return i
#return primes
def prime_factors(number):
primes = []
if (number <=1):
return [1]
a = np.ones(number)
a[0]=0
a[1]=0#not prime
for i in range(2,int(math.ceil(math.sqrt(number)))):
if(a[i]==1):
j = i**2 #cross out all the multiples
while(j < number):
a[j] = False
j+=i
for k in range(2, number):
#is prime is a factor
if(a[k]==1) and (number%k==0):
primes.append(k)
return primes
def lpf(number):
factor = 2
while (number > factor):
if(number % factor == 0):
number = number/factor
factor = 2
else:
factor +=1
return factor
out = lpf(600851475143)
print out
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