Vocabulary
Product – An answer to a
multiplication problem.
7 x 8 = 56
Product
Vocabulary
Factor – a number that is
multiplied by another to
give a product.
7 x 8 = 56
Factors
Vocabulary
Factor – a number that
divides evenly into another.
56 ÷ 8 = 7
Factor
Vocabulary
Prime Number – a number
that has only two factors, 1
and itself.
5
5 is prime because the only
numbers
that will divide into it evenly
are 1 and 5.
Prime Numbers:
Eratosthenes’s
Sieve
Eratosthenes
(ehr-uh-TAHS-thuh-neez)
Eratosthenes was a librarian from
Alexandria, Egypt in 200 B.C.E
Note: every book was a scroll.
Eratosthenes
(ehr-uh-TAHS-thuh-neez)
Eratosthenes was a Greek
mathematician, astronomer, and
geographer.
He invented a method for finding
prime numbers that is still used
today.
This method is called
Eratosthenes’ Sieve.
Eratosthenes’ Sieve
A sieve has holes in it and is
used to filter out the liquid.
Eratosthenes’s sieve filters out
numbers to find the prime
numbers.
Hundreds Chart
On graph paper, make a chart
of the numbers from 1 to 100,
with 10 numbers in each row.
4–
5;
cross
out
of
1–Leave
–Leave
Cross
1; it
is multiples
not
prime.
23–
5–
2;out
7;
cross
out
multiples
of537
2
Leave
3;
cross
out
multiples
of
All
the
numbers
left
are
prime!
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99 100
The Prime Numbers from 1
to 100 are as follows:
2, 3, 5, 7, 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47,
53, 59, 61, 67, 71, 73,
79, 83, 89, 97
Factors, Primes, &
Composite Numbers
Vocabulary
Composite number – a number
that has more than two factors.
8
The factors of 8 are 1, 2, 4, 8
Examples of Composite
Numbers
4, 6, 8, 9, 10, 12, 14, 15
Special Note:
Every whole number from 2 on is
either composite or prime.
1 is the Loneliest Number
It is not prime
because it does
not have
exactly
two different
factors.
It is not
composite
because it does
not have more
than 2 factors.
One is not a prime nor
a composite number.
Definition
Prime Factorization – A way
to write a composite number
as the product of prime
factors.
2 x 2 x 3 = 12
2
or
2 x 3 = 12
How to Do Prime Factorization
Using a Factor Tree
Step 1: Begin
with a composite
number.
Step 2: Find two
factors that can
be multiplied to
make that
number
4
36
9
2 x 2x3 x 3=36
2
2
2 x 3 = 36
Step 3: continue
finding factors
until all are
prime.
Step 4: rewrite
using exponents.
Prime Factorization
There is More Than One Way…
4
36
36
36
9
2 2 3 3
2
18
6
6
2 3 2 3
2 9
3 3
…but the prime factorization will
always be the same.
2
2
x
2
3
=36
Prime Factorization
How to Do Prime Factorization
Using a Factor Tree
Step 1: Begin
with a composite
number.
54
9
6
2 x 3x3 x 3=54
3
2 x 3 = 54
Step 2: Find two
factors that can
be multiplied to
make that
number
Step 3: continue
finding factors
until all are
prime.
Step 4: rewrite
using exponents.
Prime Factorization
How to Do Prime Factorization
Using a Factor Tree
Step 1: Begin
with a composite
number.
Step 2: Find two
factors that can
be multiplied to
make that
number
Step 3: continue
finding factors
until all are
prime.
Step 4: rewrite
using exponents.
6
48
8
4
3 2
4
2 x 3 =48 2 2
2
Prime Factorization