Transcript The Ladder Method

FACTORS
AND
GREATEST COMMONFACTORS
(GCF)
What is a Factor
• A whole number that divides exactly
into another number
ARRANGEMENT OF
STARS
• Take 6 stars and arrange
them in different
ways
• 1 Row × 6 Stars/Row = 6 Stars
• 3 Rows × 2 Stars per row = 6 stars
• 2 Rows × 3 stars per row = 6 stars
• 6 Rows × 1 Star/Row = 6 Stars
As we can see, 6 can be
written as product of two
numbers in many ways:
6 = 1 × 6
6 = 2 × 3
6 = 3 × 2
6 = 6 × 1
• 1, 2, 3 and 6 are exact divisors of 6
GREATEST COMMON
FACTOR (GCF))
• The largest factor that two or more
numbers have in common.
Two different methods
1 ----LIST
2 ----LADDER
The list Method
• Step 1: Find the Factors
• Step 2: Circle Common Factors
• Step 3: Group the Greatest Factor
24 – 1,2,3,4,6,8,12,24
36 – 1,2,3,4,6,9,12,18,36
The Ladder
Method
The Ladder Method...
is a method of factoring which allows
you to factor two numbers at once in
order to…
• find the LCM of the two numbers
• find the GCF of the two numbers
• simplify a fraction with these numbers as
numerator and denominator
• Use the distributive property
Use the ladder to factor
6 and 8
You will divide out any common factors
of the two numbers
What
goes
Nownumber
divide both
Does
any6#
besides
1
into
both
and
8?
No?
Then
you
are
done.
6 and
by the
2 4?
go
into 8both
3 and
ONE YOU’RE DONE
What about the Greatest Common
Factor (GCF) of 6 and 8?
The GCF is the product of all the
numbers on the left.
The GCF
of
6 and 8
is 2.
Which numbers in the ladder
give you the GCF?
Multiply the
numbers on the
left only for
the GCF.
GCF IS ON THE LEFT
Multiply ALL the numbers on the
left
Let’s try some bigger numbers.
Divide out all the common factors down
the left side.
What number
goes
intoany
both
Does
#
24 besides
and 60?1
go
intoabout
both
How
12
and 15?
30?
6 and
No? One
Anything else?
You’re done.
Find the GCF.
x
12=
x
The GCF
of
24 and 60
is 12.
POINTS TO REMEMBER
• 1 is a factor of every number.
• Every factor of a number is an exact
divisor of that number.
• Every factor is less than or equal to
the given number.
• Number of factors of a given number
are finite.