The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

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WORKSHEET 1.10: WRITING PRIME FACTORIZATION

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Every composite number can be written as a product of prime numbers. This is called ‘‘prime

factorization.’’ To write the prime factorization of a composite number, follow these steps:

1. Find two factors of the composite number.


2. Factor each of the factors (if possible).


3. Continue this process until all of the factors are prime numbers.
   Here are the first ten prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

EXAMPLE

Find the prime factorization of 200. (Note:In the example, the prime numbers that are used to

write the prime factorization are underlined.)

• Two factors of 200 are 10 and 20. 10 × 20 = 200.


• The prime factors of 10 are 2 and 5.^2 ×^5 =^10.


• Two factors of 20 are 4 and 5.^4 ×^5 =^20. 5 is a prime number but 4 is a
  composite number and must be factored.


• The two prime factors of 4 are 2 and 2.^2 ×^2 =^4.


• Write the prime factorization by writing all of the prime factors. Therefore, the prime
  factorization of 200 = 2 × 2 × 2 × 5 × 5 or 23 × 52.

DIRECTIONS: Find the prime factorization of each number.

1. 70 2. 28 3. 60 4. 100 5. 81


2. 45 7. 75 8. 24 9. 300 10. 126

CHALLENGE:What is the smallest number that can be expressed as the

product of two different prime numbers?

21

Copyright

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.