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From www.mathisfun.com
Why find Prime Factors?A prime number can only be divided by 1 or itself, so it cannot be factored any further! Every other whole number can be broken down into prime number factors. It is like the Prime Numbers are the basic building blocks of all numbers. This idea can be very useful when working with big numbers, such as in Cryptography.Cryptography is the study of secret codes. Prime Factorization is very important to people who try to make (or break) secret codes based on numbers. That is because factoring very large numbers is very hard, and can take computers a long time to do. If you want to know more, the subject is "encryption" or "cryptography". A longer answer at this site: http://mathforum.org/library/drmath/view/57182.html More information from this site: https://www.eduplace.com/math/mw/background/6/03/te_6_03_fractions_ask.htmlFactors and Fractions: When Students Ask **Why do I need to know about prime numbers and prime factorization?** You can use the prime factorization of a number to find the LCM and GCF of two or more numbers. As you continue to study mathematics, you will find that many patterns, formulas, and number concepts in number theory rely on prime numbers and the ability to express a number as a product of prime numbers. For example, a mathematician named Goldbach made a conjecture that every even number greater than 4 can be written as the sum of two odd prime numbers. Examples of the Goldbach conjecture are 42 = 13 + 29, 66 = 19 + 47, and 120 = 59 + 61. This conjecture has never been proved or disproved.**When would I use the least common multiple?** When adding fractions, you may need to find a common denominator. You can find the least common denominator by finding the LCM of the denominators of the fractions to be added. You can also use the LCM when comparing fractions, by writing them as equivalent fractions, using the LCM of the denominators.**When do I use the greatest common factor?** A common use of the GCF is to simplify a fraction by dividing both the numerator and denominator by the GCF of both. Another way to find the LCM for two numbers is to divide the product of the two numbers by the GCF for the numbers. For example, the GCF of 36 and 60 is 12. The product of 36 x 60 = 2,160. Therefore, the LCM of 36 and 60 is 2160 ÷ 12, or 180.
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