Positive Numbers and the Number Line

Unit 1 – Prime Factorization

Vocabulary Prime Number – A number, greater than 1, with two distinct factors, one and itself. Composite Numbers – A whole number, greater than 1, with more than two factors. Prime Factorization– A method of writing a composite number as the product of its prime factors. Factor Tree – a method used to find the prime numbers within a composite number

Prime vs. Composite Example Identify whether each number is prime or composite. 23 23 is prime because the only factors of it are 1 and 23. 40 40 is composite because the factors of it are 1, 2, 4, 5, 8, 10, 20 and 40.

Prime Factorization Example Write the prime factorization of each number. Use a factor tree to help you. 56 7 × 8 4 × 2 2 × 2 23 × 7

Prime Factorization Example Write the prime factorization of each number. Use a factor tree to help you. 56 2 × 28 14 × 2 7 × 2 We did the question differently and still go the same answer!! Math is so cool 23 × 7

Prime Factorization Example Write the prime factorization of each number. Use a factor tree to help you. 24 6 × 4 3 × 2 2 × 2 Whenever possible use exponents and always write the numbers in ascending order. 23 × 3

Prime Factorization Independent Practice Rewrite each number as the product of its primes. 27 36 33 22 × 32 52 132 22 × 13 22 × 3 × 11

Working Backwards with Prime Factorization Find the number with the given prime factorization 2 × 2 × 7 22 × 3 × 11 28 132 2. 2 × 5 × 7 4. 32 × 5 × 11 70 495 Just multiply the numbers! Remember that 32 means 3 × 3

Problem Solving with Prime Factorization The width of a swimming pool (in feet) is a prime number greater than 12. The width and the length of the pool are factors of 204. What are the dimensions of the pool? 204 2 × 102 3 × 34 17 × 2 The dimensions of the pool are 17 feet by 12 feet. The 17 is the only prime number greater than 12 and the 12 is the rest of the numbers multiplied together.

Problem Solving with Prime Factorization Sometimes you can think about the relationships between numbers and save yourself a little bit of work…let me show you what I mean in terms of prime factorization The PF of 25 is 5 × 5 The PF of 50 is 2 × 5 × 5 What is the difference between them? How might you have figured out the PF for 50 without making a factor tree for it?

Problem Solving with Prime Factorization The Prime Factorization of 45 is 3 × 3 × 5. What is the Prime Factorization of 450? 2 × 3 × 3 × 5 × 5 The Prime Factorization of 200 is 2 × 2 × 2 × 5 × 5. what is the Prime Factorization of 100? 2 × 2 × 5 × 5