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. 

Hint $\ $ Prime $\rm\:p\neq 2,3\:\Rightarrow\: p\equiv \pm 1\pmod 6$
Remark $\ $ For more on sieving see my post here, which includes links to ingenenious mechanical sieving machines devised by Lehmer in the precomputer era, e.g. using bicycles chains, photoelectric devices, etc. Below are some general references.
Wooding, Kjell. The Sieve Problem in One and Two-Dimensions.
PhD Thesis. Calgary, Alberta. April, 2010
Lehmer, D.H. The sieve problem for all-purpose computers, MTAC, v. 7 1953, p. 6-14
