### About Prime Factorization:

Whole numbers larger than one fall into one of two categories: prime or composite. A prime number is one that is only divisible by itself or one. A composite number is divisible by some number other than itself or one. It will be useful to us to be able to break a number down into the product of prime factors.

Test Objectives

- Demonstrate the ability to determine if a whole number is prime, composite, or neither
- Demonstrate the ability to construct a factor tree
- Demonstrate the ability to use a factor tree to find the prime factorization of a whole number

#1:

Instructions: Determine if each number is prime, composite, or neither.

a) 17

b) 1

c) 150

d) 12

e) 13

f) 23

g) 110

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#2:

Instructions: Write each as a product of prime factors.

a) 135

b) 1800

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#3:

Instructions: Write each as a product of prime factors.

a) 680

b) 12,600

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#4:

Instructions: Write each as a product of prime factors.

a) 468

b) 3420

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#5:

Instructions: Write each as a product of prime factors.

a) 10,296

b) 2205

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Written Solutions:

#1:

Solutions:

a) 17 - prime

b) 1 - neither

c) 150 - composite

d) 12 - composite

e) 13 - prime

f) 23 - prime

g) 110 - composite

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#2:

Solutions:

a) 135 = 3^{3} x 5

b) 1800 = 2^{3} x 3^{2} x 5^{2}

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#3:

Solutions:

a) 680 = 2^{3} x 5 x 17

b) 12,600 = 2^{3} x 3^{2} x 5^{2} x 7

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#4:

Solutions:

a) 468 = 2^{2} x 3^{2} x 13

b) 3420 = 2^{2} x 3^{2} x 5 x 19

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#5:

Solutions:

a) 10,296 = 2^{3} x 3^{2} x 11 x 13

b) 2205 = 5 x 7^{2} x 9