prime factorization

prime factorization : In number theory, integer factorization is the breaking down of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer. When the numbers are very large, no efficient integer factorization algorithm is publicly known; a 2005 effort by F. Bahr, M. Boehm, J. Franke, T. Kleinjung factored a 193-digit number ( RSA-640) utilizing 30 2.2GHz-Opteron-CPU years over a span of 5 months. The presumed difficulty of this problem is at the heart of certain algorithms in cryptography such as RSA. Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing. Not all numbers of a given length are equally hard to factor. The hardest instances of these problems (for currently known techniques) are semiprimes, the product of two prime numbers. When they are both large, randomly chosen, and about the same size (but not too close)....   More from Wikipedia

prime factorization : In mathematics, especially in number theory, quadratic integers are a generalization of the rational integers to quadratic fields. Important examples include the Gaussian integers and the Eisenstein integers. Though they have been studied for more than a hundred years, many open problems..   More from Wikipedia

  Access full lesson containing this video at: www.yourteacher.com Students learn that the prime factorization of a number is the given number written as the product of its prime factors. For example, to find the prime factorization of 45, use a factor tree to find that 45 is 5 x 9, and 9 is 3 x 3. So the prime factorization of 45 is 5 x 3 x 3, or 5 x 3^2. Note that the prime factorization of a prime number, such as 23, is the number itself....

  Using a factor tree to find the prime factorization of 72

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