Probably the simplest to implement, yet quite efficient, factoring algorithm that I know is Pollard's Rho algorithm. Both algos have these running times only in case of composite non-prime number, that's why primality test should be used to filter out prime non-factorable numbers. I used following algorithms in my code: Fermat Primality Test Fermat primality test is used before running Pollard's Rho in order to filter out prime numbers.
Trial Division is used as a fallback because Pollard's Rho in very rare cases may fail to find a factor, especially for some small numbers. Obviously after fully factorizing a number into sorted list of prime factors the largest prime factor will be the last element in this list. In general case for any random number I don't know of any other ways to find out largest prime factor besides fully factorizing a number.
As an example in my code I'm factoring first fractional digits of Pi, code factorizes this number within 1 second, and shows largest prime factor which is digits bits in size! Try it online! Here is my attempt in c. The last print out is the largest prime factor of the number.
I checked and it works. The working of the code is explained below:. Here is my approach to quickly calculate the largest prime factor. It is based on fact that modified x does not contain non-prime factors. To achieve that, we divide x as soon as a factor is found. Then, the only thing left is to return the largest factor. It would be already prime. Guess, there is no immediate way but performing a factorization, as examples above have done, i.
From certain size of f the expected search time is less, if you do a primality test on reduced N' , which in case confirms, that your N' is already the largest prime factor of initial N. Here is my attempt in Clojure. Only walking the odds for prime? Using lazy sequences help producing the values just before they are needed. It seems to me that step 2 of the algorithm given isn't going to be all that efficient an approach.
You have no reasonable expectation that it is prime. Also, the previous answer suggesting the Sieve of Eratosthenes is utterly wrong. I just wrote two programs to factor One was based on the Sieve, one was based on the following:.
The thing is, on modern processors the type of operation matters far less than the number of operations, not to mention that the algorithm above can run in cache, the Sieve can't. The Sieve uses a lot of operations striking out all the composite numbers. Note, also, that my dividing out factors as they are identified reduces the space that must be tested.
Every time you prime factorize a number, use implementation by Triptych but iterating this list of prime numbers rather than natural integers. Edit: In step 3 you can use the Sieve of Eratosthenes or Sieve of Atkins or whatever you like, but by itself the sieve won't find you the biggest prime factor. Here is the same function Triptych provided as a generator, which has also been simplified slightly.
I think it would be good to store somewhere all possible primes smaller then n and just iterate through them to find the biggest divisior. You can get primes from prime-numbers. Stack Overflow for Teams — Collaborate and share knowledge with a private group.
Create a free Team What is Teams? Collectives on Stack Overflow. Learn more. Algorithm to find Largest prime factor of a number Ask Question. Asked 13 years, 4 months ago. Active 3 months ago. Viewed k times. What is the best approach to calculating the largest prime factor of a number? Python Programs. Python How Tos. Numpy Module. Matplotlib Module. Tkinter Module. Network Programming with Python.
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Java Wrapper Class. Java 8. Java More in Java Java Compiler. Computer Sci. Computer Architecture. If we pass 15 to your program, it should return 5, and if we pass 6 to your program it should return 3. One thing to note here is that we are not handling invalid input here e. You can throw IllegalArgumentException for those inputs which are not valid as per problem specification. Similarly, you also need to include unit tests to check those invalid inputs.
I leave that task for you as practice. That's all about how to find the largest prime factor of a number in Java. This is a really good exercise to learn to code when you are starting with Java or Python or any other programming language. This kind of problem will help to build your programming logic and improve your coding skill. Believe me, it's not easy to convert a real-life algorithm into a program without practice. You must solve some basic coding problems based upon String, array, and recursion to get hold of coding.
I have shared many such exercises in this blog, if you are interested you can also take a look at the following list of problems: How to Swap Two Numbers without using Temp Variable in Java? Trick Write a program to check if LinkedList contains a loop in Java?
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Solution Write a program to check if Array contains duplicate number or not? Find the largest prime factor of a number. Python3 code to find largest prime.
A function to find largest prime factor. Initialize the maximum prime factor. Print the number of 2s that divide n. This condition is to handle the. Driver code to test above function. WriteLine maxPrimeFactors n ;.
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