August 14, 2013 Homework: Computation Sheet Column H & Addison Sheet p. 28 #’s 13-23 Warm-up: Identify whether the numbers given are prime or composite 19 9 20 37

Prime Factorization, Greatest Common Factor, & Least Common Multiple Take Notes on pg 15

The Essential Question How can I determine the prime factorization for a number? 2 3 5 10 6 180 18

Factors Factors are numbers you can multiply together to get another number. A number can have many factors Characteristics Requires at least two numbers They create numbers Examples 2 x 3 = 6 2 & 3 are factors

Factors http://www.mathsisfun.com/definitions/factor.html Non-Examples: 2 x 3 = 6 6 is a multiple not a factor 3 x 4 = 12 12 is a multiple not a factor

Prime Factorization Definition: is finding which prime numbers multiply together to make the original number. Characteristics: Can only be a prime number Can only be a factor Examples: Prime factorization of 12: 2x2x3

Prime Factorization Non-Example: 8x5 3x3x4x5

Solving for Prime Factorization, GCF, and LCM. There are 2 Ways determine the prime factors Factor Tree Method Stacked Method Determining the GCF and LCM GCF LCM

Determining the Prime Factors using the Factor Tree Method Lesson #1

Factor Tree Method 96 × 12 The CORRECT answer: 4 × 2 2 × 6 2 × 2 2 × 3 × 12 4 × 2 2 × 6 2 × 2 2 × 3 2×2×2×2×2×3 = 96 The CORRECT answer: must be only PRIME numbers must multiply to give the specified quantity

Factor Tree Method cont. There is more than one way to solve the same problem 96 × 12 4 × 2 2 × 6 2 × 2 2 × 3 96= 2×2×2×2×2×3 96 4 × 24 2 × 2 6 × 4 2 × 3 2 × 2 96= 2×2×2×2×2×3

Your Turn!! 14 7 ? 2 50 25 5 2 ? Prime Factorization for 14

Determining the Prime Factors using The Stacked Method Lesson #2

The Stacked Method Begin by dividing the specified quantity by any PRIME number that divides equally, (hint; if it is even try dividing by 2) Reduce the quotient, dividing again by a PRIME number Continue reducing the quotient until both the divisor and the quotient are prime numbers. Re-write the prime numbers as a multiplication problem. (if the final quotient is 1 it doesn’t need included in the answer) The CORRECT answer: must be only prime numbers must multiply to give the specified quantity

Stacked Method Find the Prime Factorization for 62

Exit Ticket Write Inman Style on the card Complete Prime Factorization for 72

Determining the Least Common Multiple Of Two Composite Numbers Lesson #3

Solving for the Least Common Multiple 36 3 × 12 3 × 4 2 × 2 2 × 2 × 3 × 3 = 36 54 6 × 9 2 × 3 3 × 3 2 × 3 × 3 × 3 = 54

Determining the Greatest Common Factor Of Two Composite Numbers Lesson #4

Solving for the Greatest Common Factor Find the prime factorization of the given quantities Determine what factors they have in common. 36 3 × 12 3 × 4 2 × 2 2 × 2 × 3 × 3 = 36 54 6 × 9 3 × 2 3 × 3 2 × 3 × 3 × 3 = 54

Activities for Your Portfolio Assessment Activities for Your Portfolio