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Understanding Factors: Definitions, Examples, and Prime Factorization Explained

This section covers the fundamentals of factoring numbers, listing important definitions, examples, and explanations. It defines factors, prime numbers, common factors, and greatest common factors (GCF). You will learn how to find the set of factors for a number, such as 48, and how to express integers in terms of their prime factors. Examples demonstrate the concepts clearly, making it easier for students to grasp the topic and its applications in mathematics.

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Understanding Factors: Definitions, Examples, and Prime Factorization Explained

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  1. Section 5.1Factoring Numbers

  2. Factor • When two or more numbers are multiplied, each of the numbers is a factor of the product. • Example: • 48 = 6 ● 8 6 and 8 are factors of 48

  3. Factor Set • The set of factors for a given number. • Example: • List all the positive pairs of factors of 48. {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

  4. Prime • An integer greater than 1 that has no positive integral factor other than itself and 1. • Example: 2, 3, 5, 7, 11, 13, 17,… • 0 and 1 are neither prime nor composite! 2 is the only even prime number!

  5. Prime Factorization • Expressing a positive integer as a product of primes • Example: Write the prime factorization of 48. 48 48=24 ● 3 6 8 3 2 4 2 2 2

  6. Common Factor • A factor of two or more integers • Example: • 5 is a common factor of 15 and 25 • 3 is a common factor of 6 and 18

  7. Greatest Common Factor • The common factor with the greatest coefficient and the greatest degree in each variable. • Example: • Find the GCF of 66 and 90.

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