Prime Factorization and LCM

Prime Factorization and LCM:

​by ZA

Multiple Choice

A composite number ...

• has more than 2 factors.

• has one factor.

• has at least 10 factors.

• is always a really big number.

Multiple Choice

A prime number...

• has one factor.

• has more than 2 factors.

• has 100 factors.

• has exactly 2 factors: 1 and the itself.

Watch video (approx. 2 minutes)

​

I. Prime Factorization:

Multiple Choice

Use a factor tree to find the prime factorization of 72

• 2x2x2x3x3

• 4x3x3x2

• 4x2x2x2x2

Multiple Choice

2 x 2 x 2  or 2³ is the prime factorization of

• 6

• 12

• 22

• 8

Multiple Choice

Create a factor tree and find the prime factorization for 80

• 2⁴⋅5

• 4²⋅5

• 2⋅2⋅2

• 8⋅5⋅2

Multiple Choice

Write 144 in prime factorization. Use a factor tree. Show your work.

• 2² x 3⁴

• 2⁴ x 3²

• 2³ x 3³

• 2⁴ x 3³

Multiple Choice

What number has the prime factorization of 2³ • 3² • 5?

• 360

• 720

• 180

• 240

Multiple Choice

What is the prime factorization of 20 written in exponential notation?

• 2 x 5

• 1 x 20

• 2 x 10

• 2² x 5

Multiple Choice

What is the prime factorization of 48 written in expanded notation?

• 4x2x6

• 4x2x2x3

• 3x2x2x2x2

• 12x4

Multiple Choice

Find the prime factorization of 75 in exponential form.

• 3 × 5²

• 3² × 5

• 5 × 15

• 3² × 5²

Watch video (approx. 3 minutes)

​

LCM:

Multiple Choice

Find the least common multiple of 16 and 24

• 36

• 46

• 48

• 24

Multiple Choice

Find the least common multiple of 8 and 12

• 16

• 20

• 35

• 24

Multiple Choice

Find the least common multiple of 13 and 39

• 52

• 39

• 45

• 24

Multiple Choice

LCM stands for

• least common denominator

• least common multiple

• common factor

• factor tree

Multiple Choice

What is the LCM for 4 and 7?

• 4

• 7

• 14

• 28

Multiple Choice

What is the LCM of 32 and 40?

• 180

• 160

• 140

• 200

​Now review: Laws of Exponents

Multiple Choice

Simplify a⁴(a⁵).

• a⁴⁺⁵ = a⁹

• a^4-5 = a^-1

• a⁴⁽⁵⁾ = a²⁰

• 2a⁴⁺⁵ = 2a⁹

Fill in the Blank

$$Solve\ 4^{-3\ \div}\ 4^2$$  Write answer as a fraction without exponents:

Multiple Choice

Solve and Simplify (no exponent)

$$2^0$$  

• $$0$$  

• $$1$$  

• $$2$$  

• $$\frac{1}{2}$$  

Multiple Choice

Solve and Simplify (no exponent)

$$3^{-4}\times3^3$$  

• $$\frac{1}{3^1}$$  

• $$3^{-1}$$  

• $$\frac{1}{3}$$  

• $$\frac{1}{2187}$$  

Multiple Choice

Solve and Simplify (no exponent)

$$3^{-3}$$  

• $$27$$  

• $$\frac{1}{3^3}$$  

• $$3^3$$  

• $$\frac{1}{27}$$  

Multiple Choice

Solve and Simplify (no exponent)

$$\left(2^2\right)^3$$

• $$2^6$$

• $$64$$

• $$2^5$$

• $$32$$

Multiple Choice

Solve and Simplify (no exponent)

$$2^4\cdot2^{-2}$$

• $$2^6$$

• $$2^2$$

• $$64$$

• $$4$$

Multiple Choice

$$\left(-2x^3y^2\right)\left(5xy^4\right)$$  

• $$3x^3y^8$$  

• $$3x^4y^6$$  

• $$-10x^3y^8$$  

• $$-10x^4y^6$$  

Multiple Choice

$$4z^4\cdot6z^{-6}$$  

• $$\frac{24}{z^2}$$  

• $$24z^{-24}$$  

• $$\frac{10}{z^2}$$  

• $$10z^{-24}$$  

Multiple Choice

$$\left(3xy\right)\left(xy\right)$$  

• $$x^2y^2$$  

• $$3xy$$  

• $$3x^2y^2$$  

• $$\frac{xy}{3xy}$$