{"id":5605,"date":"2013-03-20T12:15:03","date_gmt":"2013-03-20T12:15:03","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=5605"},"modified":"2014-12-02T08:27:04","modified_gmt":"2014-12-02T08:27:04","slug":"prime-numbers-and-factorization","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/prime-numbers-and-factorization\/","title":{"rendered":"Prime Numbers and Factorization"},"content":{"rendered":"

Overview:\u00a0 What Are Prime Numbers?<\/strong>
\nThe definition of a prime number is any number greater than one that can only be divided evenly by 1 and itself.. \u00a0Therefore, 2 is a prime number because its only factors are 1 and 2, and \u00a03 is a prime number because its only factors are 1 and 3.\u00a0 The number 4 is not because it has another factor than 1 and 4, the number 2.\u00a0\u00a0 It is a composite number.<\/p>\n

Why Are Prime Numbers Important?<\/strong>
\nPrime numbers are the building blocks of the natural (counting) numbers, and they are considered an important part of number theory.\u00a0 One mathematician proposed a theorem that every even \u00a0number greater than 2 is the sum of two primes, which has neither been proven or disproven. \u00a0\u00a0In fact, they are considered so essential that mathematicians have sent signals into space that are sequences of prime numbers, in the hopes that other intelligent civilizations would respond to the signal.\u00a0 (So far, there have been no responses.)\u00a0 They have applications in computer science, and are the basis for high-level codes.<\/p>\n

Why Isn’t One a Prime Number?<\/strong>
\nThe number 1 is neither a prime number nor a composite number because it doesn’t have all the properties of either primes or composites.\u00a0 In fact, the ancient Greeks, who discovered prime numbers, didn’t consider the number 1 to be a number, so it wasn’t an element of their definitions.\u00a0 One of the important theorems in arithmetic is that every number can be expressed as a unique product of primes, and there are many other arguments that follow, only if the number one is not part of the definition.<\/p>\n

Finding Prime Numbers<\/strong>
\nThe ancient Greeks, such as \u00a0Euclid, used prime numbers in the development of number theory.\u00a0 They theorized that the set of prime numbers was infinite, since the set of numbers is infinite, and there can always be one number greater. Smaller numbers are found by methods of trial division, although that method has too many variables for very large numbers.\u00a0 Computers use a different algorithm for large numbers that involve exponents and another theorem.<\/p>\n

Finding Prime Factors<\/strong>
\nIf every number (over 1) can be expressed as an unique product of prime numbers, what does that mean?\u00a0 For one thing, it means that one can factor numbers completely to find prime factors.\u00a0 Looking at the number 24, it can be factored as 3 X 8.\u00a0 Three is a prime number, but 8 is not.\u00a0 Eight is the product of 2 X 2 X 2.\u00a0 The prime factorization of 24 can be read as 24 = 3 X 2 X 2 X 2.\u00a0 Prime factors can be found by repeated division, and students can factor into prime numbers using a factor tree.\u00a0 (For fun, since the number 24 is an even number greater than 2, the 2 prime numbers added together that equal 24 are 5 and 19.)<\/p>\n

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Overview:\u00a0 What Are Prime Numbers? The definition of a prime number is any number greater than one that can only be divided evenly by 1 and itself.. \u00a0Therefore, 2 is a prime number because its only factors are 1 and 2, and \u00a03 is a prime number because its only factors are 1 and 3.\u00a0 […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[11,13],"tags":[648,1386],"class_list":["post-5605","post","type-post","status-publish","format-standard","hentry","category-math-fundamentals","category-pre-algebra","tag-factorization","tag-prime-numbers"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5605","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=5605"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5605\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=5605"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=5605"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=5605"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}