### How to Find the Greatest Common Factor

Watch more Basic Math Skills videos: http://www.howcast.com/guides/54-Basic-Math-Skills Subscribe to Howcast's YouTube Channel - http://howc.st/uLaHRS Find the largest common factor for a series of numbers or algebraic expressions. Howcast uploads the highest quality how-to videos daily! Be sure to check out our playlists for guides that interest you: http://howc.st/ytmainplaylists Subscribe to Howcast's other YouTube Channels: Howcast Health Channel - http://howc.st/HOE3aY Howcast Video Games Channel - http://howc.st/tYKKrk Howcast Tech Channel - http://howc.st/rx9FwR Howcast Food Channel - http://howc.st/umBoJX Howcast Arts & Recreation Channel - http://howc.st/vmB86i Howcast Sports & Fitness Channel - http://howc.st/vKjUjm Howcast Personal Care & Style Channel - http://howc.st/vbbNt3 Howcast empowers people with engaging, useful how-to information wherever, whenever they need to know how. Emphasizing high-quality instructional videos, Howcast brings you experts who provide accurate information in easy-to-follow tutorials on everything from makeup, hairstyling, nail art design, and soccer to parkour, skateboarding, dancing, kissing, and much, much more. Step 1: Determine for a series of numbers Factor each number in a series of numbers completely into its primes; identify the common factors for each number; and then multiply the common factors together. Tip A prime number is a positive integer that is not itself the product of two smaller positive integers. Step 2: Use 18 and 27 Use the numbers 18 and 27 as an example. The primes of 18 are three, three, and two. The primes of 27 are three, three, and three. So the greatest common factor is three times three, or nine. Step 3: Determine the greatest common factor for algebraic expressions Identify all of the common factors in a series of algebraic expressions. Step 4: factor 60x2y and 210xy2 Use the expressions the common factors of the first expression are two, two, three, five, x, x, and y. The common factors in the second expression are two, three, five, seven, x, y, and y. So the greatest common factor is two times three times five times x times y, or 30xy. Did You Know? Did you know? The third century B.C.E. mathematician Euclid developed an algorithm for finding the greatest common factor of two natural numbers or two polynomials.

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