108 Chapter 2 Fractions and Mixed Numbers: Multiplication and Division 3. Prime and Composite Numbers Two important classifications of whole numbers are prime numbers and composite numbers. Definition of Prime and Composite Numbers • A prime number is a whole number greater than 1 that has only two factors (itself and 1). • A composite number is a whole number greater than 1 that is not prime. That is, a composite number will have at least one factor other than 1 and the number itself. Note: The whole numbers 0 and 1 are neither prime nor composite. Identifying Prime and Composite Numbers Example 3 Determine whether the number is prime, composite, or neither. a. 19 b. 51 c. 1 Solution: a. The number 19 is prime because its only factors are 1 and 19. b. The number 51 is composite because . That is, 51 has factors other than 1 and 51. 3 17 51 c. The number 1 is neither prime nor composite by definition. TIP: The number 2 is the only even prime number. 2 3 10 Answers 5. Composite 6. Neither 7. Prime 8. No. The factor 10 is not a prime number. The prime factorization of 60 is 2 2 3 5. Prime numbers are used in a variety of ways in mathematics.We advise you to become familiar with the first several prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, . . . . 4. Prime Factorization In Example 1 we found four factorizations of 12. The last factorization 2 2 3 consists of only prime-number factors. Therefore, we say 2 2 3 is the prime factorization of 12. 1 12 2 6 3 4 2 2 3 Prime Factorization The prime factorization of a number is the factorization in which every factor is a prime number. Note: The order in which the factors are written does not affect the product. Skill Practice Determine whether the number is prime, composite, or neither. 5. 39 6. 0 7. 41 Concept Connections 8. Is the product the prime factorization of 60? Explain.
miller_basic_college_math_3e_ch1_3
To see the actual publication please follow the link above