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

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Presentation transcript:

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. A natural number that has more than two distinct (positive) factors is called a composite number or composite. 1 is neither prime nor composite.

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.

Be able to: Find the prime factorization of a number Methods: 1. Factor Tree 2. Stacked Division Remember the Factor Test Theorem!

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 1. Intersection of Sets 1. Venn Diagram 2. Roster Notation 2. Prime Factorization 3. Euclidean Algorithm - optional

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 1. Intersection of Sets 1. Venn Diagram 2. Roster Notation 2. Prime Factorization

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

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