The Step-by-Step Solving of Prime Factorization
Prime factorization is the process of finding what prime numbers multiply together to create another number. Prime numbers are those that can be divided only by 1 and themselves. The lowest prime numbers are 2, 3, 5, 7, 9, 11, 13 and 17. While prime factorization can be used on any whole number for purposes of simplification, it is most often used to help find the least common denominator (LCD) of two fractions because the addition or subtraction of fractions requires that they have the same denominator.
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Instructions
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Find the prime factorization of a large number by first trying to break it down into any multiples you can find. Continue breaking down the multiples, step by step, until you've reached prime numbers. Write out every prime number that is a factor, even if a particular prime number repeats more than once.
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Find the prime factorization of 225 and write out the factors. Begin by dividing 225 by 5 since it looks to be divisible by that number: 225/ 5 = 45 or 225 = 5 * 45. Work on breaking down the 45 (since 5 is already prime). Note that 45 = 5 * 9, which gives us another factor of 5. Break down the 9 into its prime factors: 3 * 3.
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Write out the prime factorization of 225 as 3 * 3 * 5 * 5 = 225 or write it as 3^2 * 5^2 = 225. Note that the factors are "3", "3", "5" and "5".
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