<p>What is the fastest way to find the factors of a number? I think it takes too long to go and find every factor of a number especially if its a large number. Is there any other way?</p>
<p>Also what is the fastest way to find the LCM and the GCF of a number?</p>
<p>There’s no such question that will ever ask for something like that.</p>
<p>Mention it, if you have one.</p>
<p>for starters, you cannot find the LCM and GCD of “a number”… you need at least 2 for that…:D</p>
<p>The fastest known method uses a quantum computer.</p>
<p>[Shor’s</a> algorithm - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Shor’s_algorithm]Shor’s”>Shor's algorithm - Wikipedia)</p>
<p>edit: I honestly didn’t realize this was in the SAT forum, not HSL! Anyway, if you want to do it quick, just use your calculator. TI-89s and above have a factor function. Otherwise, you outta just pull out factors you know: know the divisibility rules for 2, 3, 5, and 11. What remains should be small enough to guess. </p>
<p>As for finding LCM and GCF of two numbers, you’d have to factor them first. Or, if you knew one of them, the other is equal to the product of the numbers divided by it.</p>
<p>A simple and methodical algorithm for computing the greatest common divisor of two integers is Euclid’s algorithm. While it is rarely taught in American’s schools it is part of the middle school curriculum in France, and knowledge of its use is expected in standard tests in that country. The algorithm dates back to the ancient Greeks.</p>
<p>You are not expected to know the algorithm for the SAT, and so SAT problems that require you to factor numbers or to compute the gcd tend to be simple – using relatively small numbers with obvious factors, or powers of small integers and the like.</p>
<p>A good description of the algorithm is to be found at:</p>
<p>[Euclidean</a> algorithm](<a href=“http://www.math.rutgers.edu/~greenfie/gs2004/euclid.html]Euclidean”>Euclidean algorithm)</p>
<p>It’s really very simple. You divide the larger integer by the smaller one and then the smaller number by the remainder of the division, etc. until you get a zero remainder. The factor that you get with the remainder of zero in the gcd. It’s best to try an example or two to the get the hang of the algorithm. It’s not difficult to prove that the algorithm is correct.</p>