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 for 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 = 33 x 5
b) 1800 = 23 x 32 x 52
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#3:
Solutions:
a) 680 = 23 x 5 x 17
b) 12,600 = 23 x 32 x 52 x 7
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#4:
Solutions:
a) 468 = 22 x 32 x 13
b) 3420 = 22 x 32 x 5 x 19
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#5:
Solutions:
a) 10,296 = 23 x 32 x 11 x 13
b) 2205 = 32 x 5 x 72