5. EXAMPLE 3 Writing Prime Factorization Write the prime factorization of 450 . Three factor trees are shown. Notice that each factor tree produces the same prime factorization, differing only in the order of the factors. So, 450 = 2 x 3 x 3 x 5 x 5. Using exponents, the prime factorization of 450 is 2 x 3 2 x 5 2
6. GUIDED PRACTICE for Examples 2 and 3 Tell whether the number is prime or composite . If it is composite, write its prime factorization using exponents. So, 24 = Composite; It has positive factors other then 1 and itself. 2 x 2 x 2 x 3 = 2 3 x 3 6. 24 Number : 24 Factors : 1, 2, 3, 4, 6, 8, 12, 24 24 4 6 2 2 2 3 .
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12. EXAMPLE 4 Factoring a Monomial Factor the monomial 12 x 2 y . Factor 12 . 12 x 2 y = Write x 2 as x x . = 2 2 3 x x y 2 2 3 x 2 y
13. GUIDED PRACTICE for Example 4 10. 3 mn Factor the monomial. 3 mn = 11. 18 t 2 Factor 18 . 18 t 2 = 3 m n 2 3 3 t 2 = 2 3 3 t t Write t 2 as t t .
14. GUIDED PRACTICE for Example 4 13. 54 w 3 z 4 Factor the monomial. 54 w 3 z 4 = Factor 54 . 2 3 3 3 w 3 z 4 = 2 3 3 3 w w w z z z z Write z 4 as z z z z Write w 3 as w w w = 2 3 3 3 w w w z 4
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16. EXAMPLE 1 Writing Factors Members of the art club are learning to do calligraphy. Their first project is to make posters to display their new lettering style. A poster will display 36 characters in order: the 26 uppercase letters of the alphabet and the digits 0 through 9 . The art club members want the characters arranged in a rectangular display with the same number of characters in each row. You can use the factors of 36 to determine how many arrangements are possible. Lettering
17. EXAMPLE 1 Writing Factors In the situation above, how many ways can the art club arrange the 36 characters in a rectangular display with rows of equal length? List the factors of 36 by writing 36 as a product of two numbers in all possible ways. 1 36 2 18 3 12 6 4 9 The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
