ALGEBRA I NOTES
SECTION 5.1 FACTORING INTEGERS
We’re going to start factoring ( breaking down a # into its component parts ).
14  2  7
63  9  7
integral factors
14  114
63  3  21
Other factors of 63: 1, 3, 7, 9, 21, 63
1.) Factor – divisor of that #.
2.) Prime # - an integer greater than 1 that has no positive integral factor other than 1 and
itself.
We are going to find FACTOR TREES – THE PRIME FACTORIZATION OF A #.
To find the prime factorization of a # :
1.) express the integer as a product of its primes.
2.) if a prime factor occurs more than once, use an exponent.
Ex.1.) Find the prime factorization of the following:
a.) 72
b.) 108
c.) 748
d.) 640
We use the prime factorization of a number to find :
1.) Greatest Common Factor – GCF – greatest integer that is a factor of all the given
integers. A GCF is the largest number that divides all the given numbers evenly.
Ex.2.) Find the GCF of 84, 140.
84
140
1.) Find each numbers prime
factorization.
2.) To find the GCF: take
the least power of each
common factor.
Common Factor – factor of
each integer – what they
share.
Ex.3.) Find the GCF of 132, 242.
132
242
Pg.187 #26, 28, 38
26.)
88
28.)
54
Find the GCF of 54, 840.
38.) 840