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Prime Factorization and Exponents ThePrimesof YourLife ACTIVITY 2 PRACTICE Write your answerson notebook paper.Show your work. Lessonz-r 1. Which of the numbersbelowis NOT a prime number? A. 13 8.37 D. 47 c. 39 2. Which is the prime factorizationof 8l? 8.3x27 A .1 x 81 D.3x3x3x3 C.9 x9 3. Explainthe differencebetweena prime numberand a compositenumber.Include examplesin your explanation. 4. List the prime numbersbetween80 and 90. 5. List the compositenumbersbetween39 and 50. 6. To checkwhether59 is prime,Claudiadivided 59 by everyodd numberfrom 3 to 29.All of the quotientshad a remainder. a. Why did shetestwith only odd numbers? b. To be surethat 59 is prime,doessheneedto continueto divide59 by odd numbersfrom 3I to 57?Why or why not? ACTIVITY2 r unl.rar;rn#f continued 12. Desmondhas169squarebricksthathe is arrangingin rowsto makea patio.Everyrow musthavethe samenumberof bricks a. How manybricksarein eachrow? b. Describethe shapeof the patio.Explain your reasoning. 13. a. Find theprimefactorization of 132. b. Explainhow you foundthe prime factorization. 14. a. Find the prime factorizationof 180. b. Explainwhy everynaturalnumberwith a zeroin the onesplaceis a composite number. 15. fasonsaidthat anynumberthat hasI asa factormustbe a compositenumber?Do you agree?Explainyour reasoning. 16. Express eachnumberasa sumof two prime numbers. a . l0 b.22 c. 30 d. s0 17. Expresseachnumberasa differenceof two primenumbers. a.2 b.8 c. 14 d. 16 7. A certainnaturalnumberis not divisibleby 7. Can it be divisibleby A? Why or why not? 8. Determinethe prime factorizationof each number. a. 30 b. 33 c. 52 d. 72 f. 76 e.65 Explain 9. Is the number 147prime or composite? how you know 10. Is 2 x 3 x 4 the prime factorizationof 24? Explainyour reasoning. 11. List all of the numbersfrom I to 100that have 13asa factor. Activity2 . PrimeFactorization andExponents 33 Prime Factorizationand Exponents ThePrlmesof YourLlfe Lessonz-z 18. Evaluateeachexpression. a. 33 b. 92 d.261 c. 1.62 g. 115 f. 22910 g. 02s h. to7 t. two and two-tenths squared j. four to the fourth power k. sevencubed [. three cubedsquared 19. Write the prime factorizationof eachnumber. Useexponentsif needed. a.32 c. 175 e. 108 b. 3g d .1 2 0 f. r2r 20. Write 81 in exponentialform two different ways. 21. a. Write 25 in exponentialform. b. Identifr the basein the expressionthat you wrote and explainwhat it means. c. Identifr the exponentin the expressionthat you wrote and explainwhat it means. 22. Thereweretwo bacteriain a dish at the 24. Which expressionequals50? B. ls A.0s D. 50 c. 5r 25. How many factorsdoesthe number 22 x32 hive? 4.4 c.e 26. Which equationis true? A. 16: 6l C.2a:42 B. 23:32 D. 3a:43 27. Eachroom in a library has3abookshelves. Eachshelfholds 27books. i. Write an expressionfor the number of booksthat areshelvedin eachroom. b. H_owr-nanyrooms do you need to hold 27 x36 bobks? MATHEMATICALPRACTICES ViableArguments Construct 28. A sixth grademath studentmadethis conjecture: Everyprime number canbe expressedasthe product of two prime numbers.Do you agree with the conjecture?Why or why not? beginningof an experiment.Every 15minutes, the number of bacteriain the dish doubled. Write in exponentialform the number of bacteriain the dish two hours afterthe experimentbegan. 23. Which of the givennumbersequals25x 32? A. g0 c. 2 4 0 8.6 D. 36 B. 192 D. 288 E o P o !U E .99 !t F o co o u o o a o @ 34 Mathematics Course1, Unit I . NumberConcepts SpringBoard@