Download Finding a Prime Factorization

Math 952
3.3 "Prime Factorization"
Objectives:
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Know the Fundamental Theorem of Arithmetic.
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Be able to …nd the prime factorization of a composite number.
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Know the meaning of the term prime factorization.
Finding a Prime Factorization
The Fundamental Theorem of Arithmetic:
kEvery composite number has exactly one prime factorization.k
De…nition:
"Prime Factorization"
kThe prime factorization of a number is a factorization of that number using only prime factors.k
How to Find the Prime Factorization of a Composite Number:
1: Factor the composite number into any two factors.
2: Factor each factor that is not prime.
3: Continue this process until all factors are prime.
Example 1: (Prime Factorization)
Find the prime factorization for each of the following numbers.
a) 45
b) 94
c) 225
d) 231
f) 162
e) 700
Page: 1
Notes by Bibiana Lopez
Prealgebra by Franklin Wright
3.3
Factors of Composite Numbers
Factors of Composite Numbers:
The only factors (or divisors) of a composite number are:
1: 1 and the number itself
2: Each prime factor
3: Products formed by all combinations of the prime factors (including repeated factors)
Example 2: (Finding Factors)
For each of the following problems, …nd the prime factorization and all the factors.
a) 48
b) 130
c) 175
d) 90
Page: 2
Notes by Bibiana Lopez