Page 252 - Algebra 1

Example
1
Finding the Prime Factorization of a Number
Find the prime factorization of each number.
a. 120
SOLUTION
Method1: Listthefactorsandthentheprimefactors.
120 = 2 · 60
= 2 · 2 · 30
= 2 · 2 · 2 · 15 =2·2·2·3·5
Method2: Useafactortree.
The prime factors are 2, 2, 2, 3, and 5.
Method3: Usedivisionbyprimes.
2 120 2 60 2 30 3 15 55
1
The prime factors are 2, 2, 2, 3, and 5.
Theprimefactorizationof 120=2·2·2·3·5.
b. 924
SOLUTION
924 = 2 · 462
= 2 · 2 · 231
= 2 · 2 · 3 · 77
= 2 · 2 · 3 · 7 · 11
Theprimefactorizationof 924=2·2·3·7·11.
Prime factorization can be used when determining the greatest common factor (GCF) of monomials, which is the product of the greatest integer that divides without a remainder into the coefficients and the greatest power of each variable that divides without a remainder into each term.
Finding the GCF means finding the largest monomial that divides without a remainder into each term of a polynomial.
Hint
One method for finding the prime factorization
of a number is to divide out all 2’s first, then all 3’s, then all 5’s, and so on, if they are factors.
120
10 2534
12 22
Lesson 38 237