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1.9 Factor Strings and Prime Factorizations √ to review name-collection boxes √ to represent numbers as products of factors (factor strings) and as products of prime factors (prime factorizations) Math Message 8 + 8 and 4 x 4 are two names for the number 16. Write at least five other names for 16. 48/3 32/2 2x8 9+7 2 4 24 15 + 1 2 + 2 +2 +2+2+2+2+2 6 + 10 A factor string is a name for a number written as a product of at least two factors that are greater than 1. In a factor string, the number 1 may not be used as a factor. Here are the factor strings for 30. 2 x 15 3 x 10 5x6 2x3x5 How do you do it? Start with factor strings with only two factors. List them all. 2 x 15 3 x 10 5x6 Take a factor pair and see if one of the numbers can be made in to another factor pair. 2 x 15 = 2 x 3 x5 Keep trying to see if you can make a different combination. (no turnarounds) Find factor strings for 24. Number Factor String Length 24 6x4 2 24 8x3 2 24 12 x 2 2 24 2x2x6 3 24 2x2x3x2 4 24 4x2x3 3 The prime factorization of 24 is 2 x 2 x 2 x 3. Vocabulary Name-Collection Box A diagram that is used for writing equivalent names for a number. Factor String A number written as a product of at least two wholenumber factors. Example A factor string for the number 24 is 2 x 3 x 4. This factor string has three factors, so its length is 3. The number 1 is never part of a factor string. Prime Factorization A whole number expressed as a product of prime factors. Every whole number greater than 1 has a unique prime factorization. Example x 3. The prime factorization of 24 is 2 x 2 x 2 Length of Factor String The number of factors a factor string has is its length. Example Another factor string for 24 is 3 x 8. This factor string has two factors, so its length is 2.