WHAT’S A FACTOR?
A number that can be
divided evenly into another
number.
Will divide evenly into only some
greater numbers.
There are a limited amount of
factors for each number.
Usually identified in pairs.
Factor
Students will often identify
multiples instead of factors.
Students often miss a factor
when listing them.
WHAT’S A MULTIPLE?
A number that can be
divided evenly by another
number.
Every number has multiples
There are an infinite amount of
multiples for each number.
Created by pairs of factors.
Multiple
Multiplication
tables are just
lists of multiples.
Students will often identify
factors instead of multiples.
WHAT’S A PRIME NUMBER?
A number that can be
divided only by itself and 1.
Every number can be divided by a
prime number.
Prime numbers are the foundation
of all numbers.
Prime
Number
Students often think odd
numbers are prime
numbers.
Example: 9
Divisibility Rules
Makes All
Types of
Division
Easier!
 Long Division
 Writing a
number in
lowest terms
 GCF
 LCM
 Distributive
Property
 Simplify
Fractions
 Solving Ratios
 Much More
WHY USE PRIME NUMBERS?
Just like houses are built from bricks…
Composite numbers are built from
prime numbers…
So, we will use the prime numbers:
2, 3, 5 and sometimes 7…
To break down composite numbers.
÷
24
2
12
2
6
2
3
3
1
GREATEST COMMON FACTOR
List all of the factors of 54:
1
9
2
18
3
27
6
54
If one number is a factor of the original
number, all of its factors are factors of the
original number, too!
Ex: A peanut butter sandwich has peanut butter
on it. Peanut butter has peanuts. Since peanut
butter has peanuts and is on the peanut butter
sandwich, the peanut butter sandwich has
peanuts, too!
Since 54 has a factor of 6, then the factors of
6 (1, 2, 3, 6) are factors of 54, too.
Since 54 has the factors of 3 and 9, then the
product of 3 & 9 (3 x 9 = 27) will create a
factor of 54, too!
Using that thinking, what other factor can
you find? Enter it into your MathBerry.
6 x 3 = 18; 18 is a factor, too!
GREATEST COMMON FACTOR
What happens when we have to find factors for more
than one number AND find the GCF?
What happens, if we miss a factor?
Do you really want to find factors that don’t matter?
Let’s work smarter, not harder!
Use prime numbers:
(1)To find only the common factors
(2)To find the correct greatest common factor.
(3)Avoid making mistakes.
GREATEST COMMON FACTOR
First, let’s learn how to use the
GCF Gold Digger!
You will need the first four
prime numbers: 2, 3, 5 & 7
GREATEST COMMON FACTOR
The numbers you want to factor, go here!
Now… think like a Gold Digger!
Starting with the first prime number (2), can it divide evenly
into both of the original numbers?
(Hint: Use your divisibility rules!)
If YES, put it here.
÷
24
36
2
12
18
2
6
9
3
2
3
The quotient of 2 goes below each dividend.
DIG! Divide by 2 until you cannot divide by 2 anymore!
If NO, move to the next prime number (3) and repeat!
Once the dividends cannot be divided by any prime number, stop.
GREATEST COMMON FACTOR
Now that all common
prime number factors
have been found, use
them to ‘build’ the
Greatest Common
Factor.
2 x 2 x 3 = 12
4
12
÷
24
36
2
12
18
2
6
9
3
2
3
x
x
3
GCF =
12
GREATEST COMMON FACTOR
The numbers you want to factor, go here!
Now… think like a Gold Digger!
Starting with the first prime number (2), can it divide evenly
into both of the original numbers?
(Hint: Use your divisibility rules!)
If YES, put it here.
÷
18
90
2
9
45
3
3
15
3
1
5
The quotient of 2 goes below each dividend.
DIG! Divide by 2 until you cannot divide by 2 anymore!
If NO, move to the next prime number (3) and repeat!
Once the dividends cannot be divided by any prime number, stop.
GREATEST COMMON FACTOR
Now that all common
prime number factors
have been found, use
them to ‘build’ the
Greatest Common
Factor.
2 x 3 x 3 = 18
6
18
÷
18
90
2
9
45
3
3
15
3
1
5
x
x
3
GCF =
18
GREATEST COMMON FACTOR
The numbers you want to factor, go here!
Now… think like a Gold Digger!
Starting with the first prime number (2), can it divide evenly
into both of the original numbers?
(Hint: Use your divisibility rules!)
If YES, put it here.
÷
50
90
2
25
45
5
5
9
The quotient of 2 goes below each dividend.
DIG! Divide by 2 until you cannot divide by 2 anymore!
If NO, move to the next prime number (3) and repeat!
Once the dividends cannot be divided by any prime number, stop.
GREATEST COMMON FACTOR
Now that all common
prime number factors
have been found, use
them to ‘build’ the
Greatest Common
Factor.
2 x 5 = 10
10
÷
50
90
2
25
45
5
5
9
x
GCF =
10
NOW, YOU TRY!
Show your work on your
white board and enter
your answer into your
MathBerries!
9
÷
45
99
3
15
33
3
5
11
x
3x3=9
GCF =
9
The following slides are not needed for this
unit, but provide challenging work through
application of prime numbers to factoring.
Attention to detail is needed.
FACTORING USING PRIME NUMBERS
(1) Find all prime number factors for the number.
(2) List 1.
(3) List each factor from the chart once.
(4) Multiply each row across.
2 x 25 = 50
5 x 5 = 25
(5) Multiply as many combinations of the prime
number factors from the chart, as you can to find
any remaining composite factors.
2 x 5 = 10
5 x 5 = 25
÷
50
2
25
5
5
FACTORING USING PRIME NUMBERS
(1) Find all prime number factors for the number.
(2) List 1.
(3) List each factor from the chart once.
(4) Multiply each row across.
2 x 12 = 24
2 x 6 = 12
2x3=6
(5) Multiply as many combinations of the prime number
factors from the chart, as you can to find any remaining
composite factors.
2x2=4
2x3=6
2x2x2=8
2 x 2 x 3 = 12
2 x 2 x 2 x 3 = 24
÷
24
2
12
2
6
2
3
FACTORING USING PRIME NUMBERS
(1) Find all prime number factors for the number.
(2) List 1.
(3) List each factor from the chart once.
(4) Multiply each row across.
2 x 18 = 36
2 x 9 = 18
3x3=9
3x1=3
(5) Multiply as many combinations of the prime number factors
from the chart, as you can to find any remaining composite
factors.
2x2=4
2x3=6
2 x 2 x 3 = 12
2 x 3 x 3 = 18
2 x 2 x 2 x 3 = 36
÷
36
2
18
2
9
3
3
3
1
NOW, YOU TRY!
(1) Find all prime number factors for the number.
(2) List 1.
(3) List each factor from the chart once.
(4) Multiply each row across.
2 x 9 = 18
3x3=9
3x1=3
(5) Multiply as many combinations of the prime number
factors from the chart, as you can to find any remaining
composite factors.
2x3=6
3x3=9
2 x 3 x 3 = 18
÷
18
2
9
3
3
3
1
NOW, YOU TRY!
(1) Find all prime number factors for the number.
(2) List 1.
(3) List each factor from the chart once.
(4) Multiply each row across.
2 x 45 = 90
3 x 15 = 45
3 x 5 = 15
5x1=5
(5) Multiply as many combinations of the prime
number factors from the chart, as you can to
find any remaining composite factors.
2x3=6
2 x 5 = 10
3x3=9
3 x 5 = 15
2 x 3 x 3 = 18 2 x 3 x 5 = 30
3 x 3 x 5 = 45 2 x 3 x 3 x 5 = 90
÷
90
2
45
3
15
3
5
5
1