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Find the Largest Prime Factor of a Number

Certification: Basic Level Accuracy: 66.67% Submissions: 33 Points: 10

Write a Python program that finds the largest prime factor of a given number.

Example 1
    

  • Input: number = 56
    • 

  • Output: 7
    • 

  • Explanation: 
      

    • Step 1: Find all prime factors of 56.
      • 

    • Step 2: Divide 56 by 2 as many times as possible: 56 ÷ 2 = 28, 28 ÷ 2 = 14, 14 ÷ 2 = 7.
      • 

    • Step 3: Now we have 7, which is not divisible by 2.
      • 

    • Step 4: Check if 7 is divisible by 3 or any other prime number less than √7. It's not.
      • 

    • Step 5: Therefore, 7 is a prime number and is the largest prime factor of 56.
      • 

    • Step 6: Return 7.
      • 

    •
Example 2
    

  • Input: number = 13
    • 

  • Output: 13
    • 

  • Explanation: 
      

    • Step 1: Find all prime factors of 13.
      • 

    • Step 2: 13 is not divisible by 2, 3, or any number less than √13.
      • 

    • Step 3: Therefore, 13 is a prime number itself and is its own largest prime factor.
      • 

    • Step 4: Return 13.
      • 

    •
Constraints
    

  • 2 ≤ number ≤ 10^12
    • 

  • Time Complexity: O(sqrt(n)) where n is the input number
    • 

  • Space Complexity: O(1)
    •
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Hint
Solution

Solution Hints

    
        
  • Start by dividing the number by 2 repeatedly until it's no longer divisible
    • 
        
  • Then check for divisibility by odd numbers starting from 3
    • 
        
  • You only need to check potential factors up to the square root of the number
    •

The following are the steps to solve:


    

  • Define a function count_primes_in_range(start, end).

  • Inside the function, define a helper function to check if a number is prime.

  • If a number is less than or equal to 1, it is not prime.

  • If a number is 2 or 3, it is prime.

  • It is not prime if a number is divisible by 2 or 3.

  • Check divisibility by numbers of the form 6k±1 up to the square root of the number.

  • Iterate through the range and count prime numbers.

  • Call the function and print the result.

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