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4.2 Prime and Composite Numbers

4.2 Prime and Composite Numbers. Remember to Silence Your Cell Phone and Put It In Your Bag!. Definition of Prime and Composite Numbers. A natural number that has exactly two distinct (positive) factors is called a prime number or prime .

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4.2 Prime and Composite Numbers

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  1. 4.2 Prime and Composite Numbers Remember to Silence Your Cell Phone and Put It In Your Bag!

  2. Definition of Prime and Composite Numbers • A natural number that has exactly two distinct (positive) factors is called a primenumber or prime. • A natural number that has more than two distinct (positive) factors is called a composite number or composite. • 1 is neither prime nor composite.

  3. Fundamental Theorem of Arithmetic • Each composite number can be expressed as the product of prime numbers in exactly one way, disregarding the order of the factors. • This theorem is also called the Unique Factorization Theorem.

  4. Be able to: • Find the prime factorization of a number Methods: • Factor Tree • Stacked Division Remember the Factor Test Theorem!

  5. Definition - Greatest Common Factor • The Greatest Common Factor, GCF, of two natural numbers is the greatest natural number that is a factor of both numbers. Methods • Intersection of Sets • Venn Diagram • Roster Notation • Prime Factorization • Euclidean Algorithm - optional

  6. Definition - Least Common Multiple • The least common multiple,LCM, of two natural numbers is the smallest natural number that is a multiple of both the numbers. Methods • Intersection of Sets • Venn Diagram • Roster Notation • Prime Factorization

  7. The GCF-LCM Product Theorem • The product of the GCF and the LCM of two numbers is the product of the two numbers. or GCF(a, b)  LCM(a, b) = a  b

  8. Definition – Relatively Prime • Two numbers are relatively prime iff their GCF is 1.

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