Name______Date______period______

Test Review

Prime Factorization

A prime number is a number whose only factors are itself and 1.

Prime Factorization - a number is written as a product of all its prime factors.

“HOW TO” Write the prime factorization of 28.

•Step 1: Draw a factor tree as shown below. The branches may show any two factors of 28 except for 1 and 28.

28

4 7

•Step 2: Continue the tree until all branches end prime numbers.

28

4 7

2 2

Step 3: Write a product, using all the prime numbers at the ends of the branches.

  • The prime factorization of 28 written in expanded form is 2  2  7
  • The prime factorization of 28 written in exponential form is 22  7

1.What is the prime factorization
of 72?

A 22 33
B 23 32
C 23 33
D 24 32 / 2.The prime factorization of what number is 2  32  7?
E 42
F 48
G 126
H 378
3.Find the prime factorization of 276
/ 4.Find the prime factorization of 360

Greatest Common Factor

  1. What is the greatest common factor

of 30 and 24?

a. 2b. 4

c. 6d. 8

  1. What is the greatest common factor

of 16, 20, and 40?

a. 2

b. 4

c. 8

d. 10

  1. What is the greatest common factor

of 378 and 90?

a. 2

b. 9

c. 12

d. 18

4) Mr. Cabinet has 21 students in his class. Mrs. Fire has 35 students in her class. The teachers want to have the same number of students in groups. What is the greatest number of students that can be in a group?

Lowest Common Multiple

  1. What is the least common multiple

of 8 and 10?

a. 2

b. 16

c. 40

d. 80

  1. What is the least common multiple of 9, 10, and 15?

a. 30

b. 90

c. 45

d. 135

  1. What is the least common multiple

of 378 and 90?

a. 90

b. 378

c. 630

d. 1890

4. Hot dogs come in packs of 6 while hot dog buns come in packs of 8. What is the smallest number of hot dogs and buns that you must buy in order to have the same number of each item?

Venn diagram-Consist of circles that stand for sets of elements. Venn diagrams help you see what different sets have in common.

How To-sample problem

The list below shows the number of students who participate in band and chorus at WhiteSandsMiddle School. A total of 85 students participate in band. A total of 100 students participate in chorus. There are 61 students who participate in both.How many total students participate in band and/or chorus?

Part AUse the list above to complete the Venn diagram in the space below.

Be sure to

  • Title the diagram
  • Label each circle
  • Place the number in each section of the diagram

Questions that can help along the way

  • How many students participate in only band?
  • How many students participate in only chorus?

How many total students participate in band and/or chorus?

24 + 61 + 39 = 124

  1. In a class of 30 students, every student studies Spanish and/or French. Eighteen students study only Spanish, and 4 students study both Spanish and French.
  1. Create a Venn Diagram to show the situation.
  1. How many students study French?
  1. The list below shows the number of students who participate in football and track

at WhiteSandsMiddle School.

  • A total of 45 students participate in football
  • A total of 36 students participate in track.
  • There are 18 students who participate in both sports.

Part A

Complete the Venn diagram in the space below.

Part B

What is the total number of students who

participate in these sports?

Answer ______students