Chapter 4

Prime Factorization/Factoring

100

Is the number 15 prime or composite?

Composite

200

Write all the factors of 32.

1, 2, 4, 8, 16, 32

300

Factor the monomial 3f⁶

3 • f • f • f • f • f • f

400

Write the prime factorization of 120.

2³ • 3 • 5

500

Factor the monomial 40m²n

2³ • 5 • m • m • n

GCF

100

Find the GCF of 12 and 18.

GCF = 6

200

Find the GCF of 24, 36, 60 by using the method that lists all the factors.

24: 1, 2, 3, 4, 6, 8, 12, 24

36: 1, 2, 3, 4, 6, 9, 12, 18, 36

60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

GCF = 12

300

Find the GCF of 24, 36, 60 by using the prime factorization method.

24: 2 • 2 • 2 • 3

36: 2 • 2 • 3 • 3

60: 2 • 2 • 3 • 5

GCF = 2 • 2 • 3 = 12

400

Are the numbers 35 and 54 relatively prime? (Must show work to prove yes or no)

35: 1, 5, 7, 35

54: 1, 2, 3, 6, 9, 18, 27, 54

GCF = 1. So yes, they are relatively prime.

500

Find the GCF of the monomials 18xy² and 28x²y².

2xy²

LCM

100

Find the LCM of 6 and 10 using the method that lists the multiples.

6: 6, 12, 18, 24, 30, 36, 12, 48, 54, 60...

10: 10, 20, 30, 40, 50, 60...

LCM = 30

200

Find the LCM using the prime factorization method.

6: 2 • 3

10: 2 • 5

LCM = 2 • 3 • 5 = 30

300

Find the LCM of the monomials 9xy² and 15x²y.

LCM = 45x²y²

400

What does LCD stand for?

Least Common denominator

500

Use the LCD to determine which fraction is greater 5/6 or 7/9

5/6.

Rules of Exponents

100

8⁷ • 8⁵

8¹²

200

z⁸ ÷ z³

z⁵

300

3m⁵ • m²  /   6m³

m⁴   /   2

400

Write the expression without using a fraction bar     a² / b³

a²b^-3

500

Write the expression using only positive exponents

16x^-6y

16y / x⁶

Scientific Notation

100

Write 3,200,000 in scientific notation.

3.2 x 10⁶

200

Write 0.0007 in scientific notation.

7 x 10^-4

300

Write 8.69 x 10⁵ in standard form.

869,000

400

Write 4.15 x 10^-2 in standard form

0.0415

500

Which of these numbers are greater?

3.69 x 10⁴

3.68 x 10⁵

3.68 x 10⁵