Solving Project Euler Problem 3: Largest Prime Factor

 Problem

"The prime factors of 13195 are 5, 7, 13, and 29. What is the largest prime factor of the number 600851475143?"

Solution

A prime factor of a number is a prime number that divides the given number without leaving a remainder. In other words, prime factors are the building blocks of a number. For example, let's consider the number 36. Its prime factors are 2 and 3 because:

• 2 is a prime number, and 36 divided by 2 equals 18 (no remainder).
• 3 is a prime number, and 36 divided by 3 equals 12 (no remainder).
• There are no other prime numbers that can divide 36 without leaving a remainder.

Here is a python implementation of this:

 

 

1.      We define a function prime_factor that takes a single argument, n, representing the target number for which we want to find the largest prime factor.

2.      We start with the smallest prime number, 2, as the initial value of the prime variable.

3.      We use a while loop to continue the factorization process as long as prime * prime (a*a) is less than or equal to the current value of number. This condition ensures that we consider prime factors up to the square root of number, which is sufficient.

4.      Inside the loop, we check if the current prime number, a, divides number evenly (i.e., without a remainder). If it does, we update number by dividing it by prime a. This step repeatedly divides number by its smallest prime factors until it becomes a prime number itself.

5.      If prime does not divide number evenly, we increment prime to the next prime number.

6.      When the loop exits, number will contain the largest prime factor of the original target number.

Solving Project Euler Problems provides a great opportunity to practice coding and algorithmic thinking.