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Class Notes for Lecture Day 6
Essentials of Factoring
Factor
Prime
List of primes < 100:
Composite
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Divisible
A number is divisible by…
2
3
4
5
6
7
8
9
10
11
Larger composite numbers
…if…
The number is even (ends with 2, 4, 6, 8, or 0)
The sum of digits is divisible by 3
Half the number is even (look at last 2 digits only)
The number ends with 5 or 0
The number is even and divisible by 3
(No trick)
Half of half the number is even (look at last 3 digits only)
The sum of the digits is divisible by 9
The number ends with 0
Two of the same digits (only for numbers < 100)
The number is divisible by all factors
Factor Tree
Prime Factorization
aka (Expanded) Prime Factored Form
Find the Prime Factorization of each number.
45
98
196
700
Greatest Common Factor (GCF)
Find the Greatest Common Factor of each group of monomials.
18, 90, 252
12x5, 21x4
45x3y, 63x2z, 54xyz
Factor Pairs
Find all factor pairs of each number.
24
96
288
1
1
2
2
3
3
4
4
5
5
6
6
7
8
9
10
11
12
600
2100
Prime Polynomial
Complete Factorization (product of prime factors)
Completely factor each of the following polynomials. Factor out GCF.
Difference of Squares
Perfect Square Trinomial
Completely factor each of the following polynomials.