Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
May 02, 2015 Focus Question: How many unique prime factorizations of a number are there? Read the introduction on page 46 in your book. May 02, 2015 What do exponents do? They give us the power to write the product of repeated factors. Yesterday we found the longest string of factors for 840. How could we communicate our method to someone else? We decomposed numbers into longer and longer strings of factors until we found the longest string, which turned out to be made up of all prime numbers. May 02, 2015 Vocabulary: exponent-tells you how many times to multiply a number by itself May 02, 2015 Exponent Video Write the following without exponents: 33 x 72 x 11. 3 x 3 x 3 x 7 x7 x 11 What does it equal? 14,553 May 02, 2015 81 can be written as 9 x 9 or 92. This means that 9 is used as a factor twice. 81 can also be written as 3 x 3 x 3 x 3 or 34. This means that 3 is used as a factor four times. Which factorization is the prime factorization? 3 x 3 x 3 x 3 or 34 May 02, 2015 Write the prime factorization of 18 using exponents. 2 x 32 May 02, 2015 2,500 can be written as 50 x 50 or 502. 2,500 can also be written as 2 x 2 x 5 x 5 x 5 x5 or 22 x 54. How many times is 50 used as a factor in 502? twice May 02, 2015 How many times is 5 used as a factor in 22 x 54? How many times is 2 used? 5 is used four times and 2 is used twice. Which factorization of 2,500 is the prime factorization? 2 x 2 x 5 x 5 x 5 x 5 or 22 x 54 May 02, 2015 In the Problem today you will continue to find the prime factorization of a number and use it to answer the questions about the number. Complete the problem on page 47. Be sure to label the top of your paper as Problem 3.2. Also be sure to label the sections with the correct letters and the questions with the correct numbers. Let's complete Section A then stop. We will go over it then you can complete the rest of the page. May 02, 2015 For Question A, part 1: did everyone in your group get the same prime factorization for 36? These are some questions you should ask yourself as you determine prime factorizations: • Are all the numbers in your string prime? • Did you keep track of all the prime factors as you found them? • Did you multiply your string of numbers to check that the product was 36? • Remember, order does not matter. May 02, 2015 Complete the rest of the problem. We will check it when everyone is finished. How can we rewrite the prime factorization of 36 using exponents? 22 x 32 Do we all need to use the same strategy to find the prime factorization of a number? May 02, 2015 Name a nonprime factor of 36. What is the prime factorization of that factor? How can you tell whether a number is prime or composite by looking at its prime factorization? Give an example. If a number is prime, it has only one factor, itself, in its prime factorization. May 02, 2015 How can you tell whether a number is even or odd by looking at its prim factorization? Give an example? If there is a factor of 2 in the prime factorization, the number is even. Otherwise, it is odd. Find the prime factorization of 120. 23 x 3 x 5 May 02, 2015 What do you multiply 5 x 23 by to get 120? 3 Is 23 x 7 a factor 120? Explain. No because 7 is not in the prime factorization of 120. Is 23 x 32 x 5 a multiple of 120? Use the prime factorization of 120 to justify your reasoning. yes; the prime factorization of 120 is included in the number 23 x 32 x 5. May 02, 2015 ACE: Page 54 Questions 5-20; 31-35