Chapter 4-3 Prime Factorization UNIT 2 Chapter 4-3 Prime Factorization

****0 and 1 are neither prime or composite**** Vocabulary Prime Number – a whole number that has exactly two factors, 1 and itself Example: 3 is a prime number because the only factors of 3 = 1 • 3 11 is a prime number because the only factors of 11 = 1 • 11 *** Prime numbers are NOT always odd numbers ****0 and 1 are neither prime or composite**** Composite Number – is a whole number that has more than two factors. Example: 4 is a composite number because it’s factors are 1 x 4 and 2 x 2 12 is a composite number because it’s factors are 1•12, 2•6, 3•4

Determine whether each number is Prime or Composite. Ex. 1) 31 = Prime (because factors are 1 • 31) Ex. 2) 50 = Composite (because factors are 1x50, 2x 25, 5x10 Ex. 3) 28 =Composite (because factors are 1•28, 2•14, 4•7

Prime Factorization Prime factorization is when a composite number is expressed as the product of prime factors. One way to find the prime factorization is to use a Factor Tree.

Example of Prime Factorization 24 {write the number you are factoring at the top} 8 • 3 {choose ANY pair of whole number factors of 24} 2 • 4 {circle ALL prime number} = 2•2•2•3 {write down all prime numbers} 2 • 2 = 2 3 •3 {use exponents, if possible for final answer

Let’s Try Some Examples Determine if the given number is Prime or Composite. Ex. 1) 11 Ex. 2) 49 Ex. 3) 83 Write the Prime Factorization for each number. Use exponents for repeated factors. Ex. 4) 33 Ex. 5) 66 Ex. 6) 63

Let’s Check Our Answers! Determine if the given number is Prime or Composite. Ex. 1) 11 Ex. 2) 49 Ex. 3) 83 Prime Composite Prime Write the Prime Factorization for each number. Use exponents for repeated factors. Ex. 4) 33 Ex. 5) 66 Ex. 6) 63 3 • 11 2•3•11 3 2 • 7