Transcript prime and composite numbers

Warm Up
#1. We have 22 students in this class, how
many ways could Ms. Fraser group
everyone so that all the groups are equal?
What if we had one more student? What if
we had one less?
#2. A large restaurant can seat 164 people,
how could they be seated so that each
table has the same number of people?
Warm Up September 8

Take out a sheet of looseleaf
 Number warm up is your title
 Number from 1-8
Mil.
Hun. Thou
Ten Thou
Thousands
Hundreds
Tens
Ones
PRIME AND COMPOSITE
NUMBERS
LESSON 2
PRIME NUMBERS
 A Prime
Number can be divided evenly
only by 1, or itself.
 EXAMPLES:
 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47
COMPOSITE NUMBERS
 A Composite
Number can be divided
evenly by numbers other than 1 or itself.
 EXAMPLES:
 4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,
26,27,28,30,32,33,34,35,36,38,39,40
FACTORS
 A number
may be made by multiplying two
or more other numbers together.
 The numbers that are multiplied together
are called factors.
 EXAMPLE:
FACTORS
 A number
may be made by multiplying two
or more other numbers together.
 The numbers that are multiplied together
are called factors.
 EXAMPLE:
PRODUCT
• 3 X 4 = 12
FACTOR
FACTORS
 Therefore
PRIME numbers have 2 factors:
one and itself.
 COMPOSITE numbers have more than
two factors.
 The number ONE only has one factor (1),
therefore it is not prime nor composite but
SPECIAL.
Try these
Is the number prime or composite?
a) 9
b) 7
c) 23
d) 24
e) 57
f) 144
List all of the factors of the composite
numbers
GCF

GCF – GREATEST COMMON FACTOR

The GCF is the highest factor that two or
more numbers have in common.

EXAMPLE:
The factors of 18 are {1,2,3,6,9,18}
The factors of 24 are {1,2,3,4,6,8,12,24}


GCF

GCF – GREATEST COMMON FACTOR

The GCF is the highest factor that two or more
numbers have in common.

EXAMPLE:
The factors of 18 are {1,2,3,6,9,18}
The factors of 24 are {1,2,3,4,6,8,12,24}
The GCF is 6.



Try these
Find the Greatest Common Factor. ( GCF)
a) 28, 49
b) 32, 48
c) 24, 36
PRIME FACTORS


Factors that are prime numbers.
When a composite number is written as a
product of all of its prime factors, we have the
prime factorization of the number.
 EXAMPLE: the number 72 can be written as a
product of primes as: 72 =2x2x2x3x3 .
 The expression "2x2x2x3x3" is said to be the
prime factorization of 72.
TRY THIS ONE
 Find
the PRIME factors of 32
 SOLUTION:
TRY THIS ONE
 Find
the PRIME factors of 32
 SOLUTION:
32
4
2 x
x
2
x
8
2 x 2 x 2
= 25
Try these
Express the number as a product of its
prime factors.
a) 42
LCM
 LCM
– LOWEST COMMON MULTIPLE
 A common
multiple is a number that is a
multiple of two or more numbers.
 The common multiples of 3 and 4 are:
 0, 12, 24,….
LCM
 The
least common multiple (LCM) of two
numbers is the smallest number (not zero)
that is a multiple of both.
 EXAMPLE:
 Multiples
of 3: 6,9,12,15,18,21,24,…
 Multiples of 4: 8,12,16,20,24,….
 LCM of 3 and 4 is:
 The
least common multiple (LCM) of two
numbers is the smallest number (not zero)
that is a multiple of both.
 EXAMPLE:
 Multiples
of 3: 6,9,12,15,18,21,24,…
 Multiples of 4: 8,12,16,20,24,….
 LCM of 3 and 4 is: 12
Try these
Find the Lowest Common Multiple. ( LCM )
a) 18, 27 b) 10, 25
1. Two companies are using the telephone
book to choose winners for some
promotional prizes. One company
phones every 36th name and the second
company phones every 24th name.
What is the position of the first name that
wins both prizes?