Algorithm to find Largest prime factor of a number

What is the best approach to calculating the largest prime factor of a number?

I’m thinking the most efficient would be the following:

1. Find lowest prime number that divides cleanly
2. Check if result of division is prime
3. If not, find next lowest
4. Go to 2.

I’m basing this assumption on it being easier to calculate the small prime factors. Is this about right? What other approaches should I look into?

Edit: I’ve now realised that my approach is futile if there are more than 2 prime factors in play, since step 2 fails when the result is a product of two other primes, therefore a recursive algorithm is needed.

Edit again: And now I’ve realised that this does still work, because the last found prime number has to be the highest one, therefore any further testing of the non-prime result from step 2 would result in a smaller prime.