如何使用python查找素数

Question

I need to find prime factors of a given number.

first i have written code to find the factors of a given numbers and stored as list and tried to loop through the listing if the current number is a prime number or not. However, i am getting error as one parameter in is_prime function is not defined.

below the is the code written. Could someone help understand how we can find prime factors using below code.

def factors(num):
  factor=[]
  for i in range(2,num+1):
    if num%i==0:
      factor.append(i)
  return factor

num=int(input("Enter your number: "))

number=factors(num)

print("Factors for", num, "are: ", number)

def is_prime(factor):
  for n in factor:
    for i in range(2,n):
      if n%i==0:
        return False
    return True

Prime_factors=[]
prime=is_prime(factor)

if prime:
  prime_factors.append(n)

print(Prime_factors)

Answer 1

The only error I get is that factor is not a valid variable, which is true because it defined only in factors() function, and therefore is accessable only in the function scope.

More, you can take advantage of the first function to figure out if the number is prime or not. try this:

import math

def factors(num):
  factor=[]
  for i in range(1, math.isqrt(num)+1):
    if num % i == 0:
      factor.append(i)
      if i != num//i:
        factor.append(num//i)
  return factor

num=int(input("Enter your number: "))

number=factors(num)

print("Factors for", num, "are: ", number)

def is_prime(factor):
  if len(factors(factor)) == 2 and factor != 1:
      return True
  else:
      return False


prime_factors=[]

for i in number:
    if is_prime(i):
      prime_factors.append(i)

print(prime_factors)

Answer 2

There were some syntax and logical errors in your code, I have edited the code, removed factor as undefined and moved for loop out from method is_prime to make sense. The code is as follows:

def factors(num):
   factor=[]
   for i in range(2,num+1):
    if num%i==0:
     factor.append(i)
    return factor

num=int(input("Enter your number: "))

number=factors(num)

print("Factors for", num, "are: ", number)

def is_prime(n):
  for i in range(2,n):
    if n%i==0:
      return False
    return True

Prime_factors=[]

for n in number:
  if is_prime(n):
   Prime_factors.append(n)

print(Prime_factors)

Answer 3

You need to find all factors and then select if those factors are prime. You can build the factors array first and then select prime numbers out of this array like here:

import math

def factors(num):
  factor=[]
  for i in range(2,num+1):
    if num%i==0:
      factor.append(i)
  return factor

num=int(input("Enter your number: "))

number=factors(num)

print("Factors for", num, "are: ", number)

def is_prime(n):
    if n==2: 
      return True
    if n%2==0:
      return False
    return all( n%i !=0 for i in range(3, int(math.sqrt(n)+1),2))

Prime_factors=[]

for n in number:
  if is_prime(n):
   Prime_factors.append(n)

print("Prime factors are: ",Prime_factors)

Output:

Enter your number: 56
Factors for 56 are:  [2, 4, 7, 8, 14, 28, 56]
Prime factors are:  [2, 7]

Save computational time by checking for primary numbers only up to square root of the number.

Or you can save a little bit of computations and do it in one loop, plus you can check if the number is prime by start and if it is, then you do not need to check for other factors, if it is not prime, then you only need to check for half of its value:

import math

def is_prime(n):
    if n==2:
      return True
    if n%2==0:
      return False
    return all( n%i !=0 for i in range(3, int(math.sqrt(n)+1),2))

def factors(num):
  factor=[]
  if is_prime(num):
    factor.append(num)
  else:
    for i in range(2,int((num+1)/2)):
      if num%i==0 and is_prime(i):
        factor.append(i)
  return factor

num=int(input("Enter your number: "))

factors=factors(num)

print("Prime factors are: ",factors)

And the output is now:

Enter your number: 17
Prime factors are:  [17]
Enter your number: 116
Prime factors are:  [2, 29]