1.1 prime numbers
-every number can be written as a product of primes called prime factorization
-prime factorization can be shown in many ways: factor trees & division tables
Division Tables (2772=2x2x3x3x7x11)
2
2
3
3
7
2772
1386
693
231
77
11
Factor Trees (180=2x2x3x3)
180
20 x 9
5 x 4 3 x 3
2 x 2
1.2 Greatest Common Factor and Least Common Multiple
-factors are finite #’s, always on the smaller side
-multiples are infinite #’s, always larger
-GCF = greatest common factor
-LCM = lowest common multiple
GCF of 48 and 72: 24 GCF of 90 and 225: 45
48= 2 x 2 x 2 x2x 3 FIND 90= 2 1 x 3 2 x 5 1 (2x3x3x5) CHOOSE THE ONE WITH
72= 2 x 2 x 2 x3x 3 DOUBLES 225= 2 0 x 3 2 x 5 2 (3x3x5x5) THE SMALLEST EXPONENT
GCF= 2x2x2x3 GCF= 3x3x5
= 24 = 45

LCM of 8 and 10: 40 LCM of 10 and 12 and 14: 420
8= 2 x2x2 MULTIPLY WHAT THEY HAVE 10= 2x5 12= 2x2x3 14= 2x7
10= 2 x5 IN COMMON BY WHAT’S LEFT OVER 10= 2 1 x 3 0 x 5 1 x 7 0 CHOOSE THE ONE WITH
LCM= 2 x2x2x5 12= 2 2 x 3 1 x 5 0 x 7 0 THE BIGGEST EXPONENT
= 40 14= 2 1 x 3 0 x 5 0 x 7 1
LCM= 2x2x3x5x7
= 420
1.3/1.4 Number Systems
-all #’s can be grouped based on their decimal representations
- R = real numbers
- Q = quotients, rational #’s (fractions, terminating or repeating decimals)
- Q with a line over it = quotients, irrational #’s (non-terminating decimals, can’t be fractions)
- Integers = something that could be found on a number line, negative or positive numbers
- Whole Numbers
- Natural Numbers = something you’re taught as a child (positive, whole numbers)
1.5 Radicals
4 3 √ 10 - index = 3 radicand = 10 coefficient = 4 square root sign= radical sign
when there’s no index it’s an imaginary 2
√9 = 3 because 3x3=9
5 √1/32 – 5 √1 / 5 √32 = ½ because 1x1x1x1x1 = 1 and 2x2x2x2x2 = 32
Simplify:
√40 = √ 2x2 x2x5 LOOK FOR PERFECT √32 / √8 = √2X2X2X2X2 / √2X2X2
= √4 x √10 SQUARES = √4 x √4 x √2
√40 = 2√10 √4 x √2 CANCEL OUT
= √4 ---- √32 / √8 = 2

1.6 Mixed and Whole Radicals
Simplify: √45 = 3√5 2/3 √63 = 2√7
√9 x √5 2/3 √9 x √7
3 √5 2/ 3 x 3 x √7
2 x √7
1.7 More Mixed and Whole Radicals
3 √54 = 3 3 √2 4 3 √2 = 3 √128
54= 2x 3 x 3 x 3 FIND THE 3 √64 X 3 √2 = (64 x 2)
PERFECT CUBES = 128
Perfect Cubes: Perfect Squares:
1 3 = 1 6 3 = 216 4 100
2 3 = 8 7 3 = 343 9 121
3 3 = 27 8 3 = 512 16 144
4 3 = 64 9 3 = 729 25 169
5 3 = 125 10 3 = 1000 36 196
49 225
64 256
81 289