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
Factoring Whole Numbers Test:
#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
#2:
Instructions: Write each as a product of prime factors.
a) 135
b) 1800
#3:
Instructions: Write each as a product of prime factors.
a) 680
b) 12,600
#4:
Instructions: Write each as a product of prime factors.
a) 468
b) 3420
#5:
Instructions: Write each as a product of prime factors.
a) 10,296
b) 2205
Written Solutions:
Solution:
a) 17 - prime
b) 1 - neither
c) 150 - composite
d) 12 - composite
e) 13 - prime
f) 23 - prime
g) 110 - composite
Solution:
a) 135 = 3^{3} x 5
b) 1800 = 2^{3} x 3^{2} x 5^{2}
Solution:
a) 680 = 2^{3} x 5 x 17
b) 12,600 = 2^{3} x 3^{2} x 5^{2} x 7
Solution:
a) 468 = 2^{2} x 3^{2} x 13
b) 3420 = 2^{2} x 3^{2} x 5 x 19
Solution:
a) 10,296 = 2^{3} x 3^{2} x 11 x 13
b) 2205 = 5 x 7^{2} x 9