Write the prime factorization for 65,169

Let's try to find some primes that divide this number.

The number is not divisible by 2, because it is odd.

The number is divisible by 3 though, because the sum of its digits is:

So, we can divide the number by 3 and keep going with the factorization:

This number is again divisible by 3, because

We have

This number is no longer divisible by 3. Let's go on looking for primes that divide it: 5 doesn't because the number doesn't end in 0 nor 5. This number is not divisible by 7 or 11 either (just try). It is divisible by 13 though: we have

And 557 is prime, so we're done. This means that the prime factorization of 65169 is