Test 3 Study Guide
Factors, Multiples, GCF, LCM
Name:________________________
Parent Signature:_______________
I can…find factors of whole numbers. I can…list multiples of whole numbers
What is a factor? The numbers that are multiplied
together are called factors. Also, a factor is a number
that will divide evenly into another number.
Give it a try!
T-chart
24
For example, the factors of 12 are: 1,2,3,4,6,12
Methods for listing all the factors of a number are using a
t-chart and rainbow.
18
1
18
2
9
3
6
1, 2, 3, 6, 9, 18
Rainbow method
36 =
*Four is a factor of 12. (Remember replace “factor” with
“will go into”.)
*Twelve is NOT a factor of 4. (Because 12 will NOT “go
into” 4.)
What is a multiple? A number that is multiplied by the
counting numbers. Remember multiples never end…
(dot, dot, dot)
Multiples always start with x1. Multiples
“multiply”…they get bigger and bigger!
Example:
4= 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48…
Directions: List the first 10 multiples of 7.
7, 14, 21, 28, 35, 42, 49, 56, 63, and 70
*Seventy-seven is a multiple of 11. (Because 11 x 7
equals 77.)
*Four is NOT a multiple of 12. (Remember a multiple has
to be equal to the number or larger…not smaller!)
Give it a try!
List the first 7 multiples of 8.
_________________________________________
List the multiples of 5
_________________________________________
What is the 4th multiple of 9?
_________________________________________
What is the second multiple of 12?
_________________________________________
I can…find the greatest common factor of 2 numbers. I can…find the least common multiple of 2 numbers.
Greatest Common Factor – GCF – The greatest common factor
is the greatest (largest, biggest) number that will evenly go into
a set of numbers.
Give it a try!
Find the GCF of 9 and 12. (Use the listing
method.)
Methods for finding the GCF are: listing, T-chart, Cake method.
#1 – List the factors of each number. See what factors they
have in common…and the “greatest” factor is the GCF
Ex: What is the GCF of 12 and 18?
12 – 1, 2, 3, 4, 6, 12
GCF (12, 18) = 6
18 – 1, 2, 3, 6, 9, 18
#2 – Use a T-chart to find the GCF
12
6
4
1
2
8
4
.
3
Find the GCF of 24 and 36. (Use the t-chart
method.)
24
36
GCF (12, 8) = 4
#3 – The B-day Cake method (FUN!)
2
GCF (9, 12) = _____
8
12
1
2
3
9 = ________________________________
12=________________________________
Find the GCF of 16 and 24. (Use the cake
method.)
12, 18
6, 9
2, 3
GCF(12, 18) = 2x3 = 6
Least Common Multiple – LCM – The least common multiple
is the smallest (least) multiple a set of numbers has in
common.
Methods for finding the LCM are: Listing and Cake Method
#1 – When listing the multiples of each number, list a few at a
time and stop when the same multiple appears in each list!
4 = 4, 8, 12, 16, 20, 24…
LCM (4, 5) = 20
5 = 5, 10, 15, 20, 25…
Give it a try!
Find the LCM of 8 and 12. (Use the listing
method)
8 - __________________________________
12-__________________________________
LCM (8, 12) = ______
Find the LCM of 4 and 12. (Use the Cake
method.)
#2 – When using the Cake method, you use the same process
as with GCF. Just remember…”with Least common multiple,
you can’t Leave anything out”…which creates an “L” in the cake
method.
3
12, 9
4, 3
LCM(12, 9) = 3x4x3 = 36
GCF & LCM Word Problem Key Words
GCF Words
Greatest, maximum,
largest, biggest
LCM words
Least, first, first
time, smallest