Question

Solving Project Euler #3.

Answer 1

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The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143?
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Answer 2

I started working with a smaller number for simplicity, such as 136.

1. Make a list of all divisors of the number.
136 = 2^3 * 17 ---> 8 divisors
{1, 2, 4, 8, 17, 34, 68, 136}

2. Now that we have a list of divisors, let's begin to sort out all the composite factors. How do we do that? Well, we first remove 1 from the set of divisors \(S\) and call that \(S'\).

Now, a composite factor here would be one that can be expressed as the product of elements in \(S'\). We remove all those. How?

We create a set of all such products. And then we remove the common elements from \(S'\) and get a list of prime factors.