List All the Factors for the Number

Primetime

Short Answer

List all the factors for the number.

3.a. List the factors of 16 and the factors of 28.

b. Complete the Venn diagram.

c. What is the greatest common factor of 16 and 28?

4. Two radio stations are playing the #1 hit song “2 Nice 2 B True” by Anita and the Goody-2-Shoes. WMTH plays the song every 18 minutes. WMSU plays the song every 24 minutes. Both stations play the song at 3:00 P.M. When is the next time the stations will play the song at the same time?

5. Judith is planning a party for her younger brother. She has 36 prizes and 24 balloons. How many children can she have at the party so that each child gets an equal number of prizes and an equal number of balloons? Explain your answer. 6. Find the prime factorization of the following two numbers. Show your work.

a.72 b.132

7. “Sam” and “Martha” are the local names for two lighthouses that guard a particularly dangerous part of the coast. Sam blinks every 12 seconds and Martha blinks every 8 seconds. They blink together at midnight. How many seconds will pass before they blink together again?

8. Carlos is packing sacks for treats at Halloween. Each sack has to have exactly the same stuff in it or the neighborhood kids complain. He has on hand 96 small candy bars and 64 small popcorn balls. a. What is the greatest number of treat sacks he can make?

b. How many of each kind of treat is in one sack?

9. Gloomy Toothpaste comes in two sizes: 9 ounces for $0.89 and 12 ounces for $1.15.

a. Ben and Aaron bought the same amount of toothpaste. Ben bought only 9-ounce tubes, and Aaron bought only 12-ounce tubes. What is the smallest possible number of tubes each boy bought? (Hint: Use your knowledge of multiples to help you.)

b. Which size tube is the better buy? 10. Vicente made three-dozen cookies for the student council bake sale. He wants to package them in small bags with the same number of cookies in each bag.

a. List all the ways Vicente can package the cookies.

b. If you were Vicente, how many cookies would you put in each bag? Why?

c. Vicente spent $5.40 on ingredients for the cookies. The student council will pay him back for the money he spent. For each of the answers in part (a), determine how much the student council should charge for each bag of cookies so they make a profit yet still get students to buy the cookies.

11. a. Write the prime factorization of 900.

12. Jack plays on a basketball team after school (or on the weekend) every third day of the month. He baby- sits his younger brother after school every seventh day of the month. How many times during a 30-day month, if any, will Jack have a conflict between basketball and babysitting? Explain your reasoning.

13. Find the least common multiple and the greatest common factor for each pair of numbers:

a. 8 and 12 b. 7 and 15 c. 11 and 17

Multiple Choice Identify the choice that best completes the statement or answers the question. Show all of your work in order to receive full credit!

____ 14. What is the greatest common factor of 16 and 28?

a.2 b.3 c.4 d.112

____ 15. Which of the following is a factor of 44? a.8 b.11 c.14 d.24

____ 16. How many different factors does 20 have? a.2 b.3 c.4 d.6

____ 17. What is the least common multiple of 18 and 28? a.2 b.9 c.252 d.504

____ 18. The local reader’s club has a set of 28 hardback books and a set of 44 paperbacks. Each set can be divided equally among the club members. What is the greatest possible number of club members? a.308 b.4 c.2 d.8 ____ 19. Alejandro and Jean are distributing erasers and pencils to the art class. There are 40 erasers and 25 pencils. Each student receives the same number of pencils and the same number of erasers, and no supplies are left over. What is the greatest number of students in the class? a. 10 students c. 65 students b. 200 students d. 5 students

20. Jennifer and Melissa are both moving and must pack their collections of CDs. Jennifer has 9 boxes and 108 CDs, while Melissa has 5 boxes and 193 CDs. Can each of them divide their CDs evenly among their boxes? Explain.