Factors and Multiples
Goal for your child: Your child will need to know the difference between a
factor and a multiple in order to apply it to future math problems like know a
prime or composite number and operating with fractions.
Vocabulary:
Factors: numbers that multiply together to give you a multiple.
Example: Factors of 18 are 9x2. 6x3. 18x1 (1,2,3,6,9,18)
Multiples: numbers that are the answer when you multiply two factors together.
Example: Multiples of 5: 5,10,15,20,25,30,35,40,45 etc.
Factor x Factor = Multiple
Prime Number: A number that only has 1 and itself as its factors.
Composite Number: A number that has more than 2 factors.
Why does my child need to know these things?
Your child will sometimes need to list the factors of a number when they need to find out if a number is
prime or composite OR when they need to simplify a fraction (see When to Apply Factors section).
Your child will need to list the multiples of a number when needing to make denominators the same in 2
fractions needing to be added or subtracted (see When to Apply Multiples section).
Prime Factorization “Cherry Tree”
Used when needing to know if a number is prime or composite
51
17
17
3
17
1
Prime Factorization: 17x3
Prime Factorization: 17x1
Composite Number
Prime Number
When to Apply Factors
AKA—find the GCF of a fraction and simplify.
GCF Checklist:

Factors of 9:
List the factors of the top and
bottom numbers.
Circle the matching factors of
the top and bottom numbers
Use the greatest circled number and divide into both the
top and bottom number of the
fraction.


9 x 1, 3 x 3
Factors of 12:
12 x 1, 3 x 4, 6 x 2
9 ÷ 3=
3
12 ÷ 3 =
4
When to Apply Multiples
LCM Checklist:





List the multiples of just the
bottom numbers
(denominators).
Circle the matching multiples
of the top and bottom numbers
Use the smallest circled number as your new denominator
(bottom number).
Create a multiplication fact and
multiply by the boxed number
to create your new fractions
with matching denominators.
Add your top numbers
together and keep your denominator the same to get
your answer.
3 x 2=
Multiples of 4:
4, 8, 12, 16, 20, 24
c
+
Multiples of 8:
8, 16, 24, 32, 40, 48
c c
4 x 2=
5 x 1=
8 x 1=
6
8
5
8
11
8
Parent Cheat Sheets—KASH—2012