Prime factorization, Composite integers. Describe how to find a prime factor of 1742399 using at most 441 integer divisions and one square root.
So far I have only square rooted 1742399 to get 1319.9996. I have also tried to find a prime number that divides 1742399 exactly; I have tried up to 71 but had no luck. Surely there is an easier way that I am missing without trying numerous prime numbers. Any help would be great, thanks. 

Note that the problem asks you do describe how you would go about factorizing 1742399 in at most 442 operations. You are not being asked to carry out all these operations yourself! I think your method of checking all primes up to the squareroot is exactly what the problem is looking for, but to be safe you should check that there are no more than 441 primes less than or equal to 1319.
