A multiple is a number that is evenly divisible by another number. Every number has an infinite number of multiples. Multiples are created in pairs of factors and multiplication tables list multiples. The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both. To find the LCM, list the multiples of each number in increasing order and the LCM is the first number they have in common. A prime number is only divisible by 1 and itself, with no other factors. Prime numbers are the foundation of all other numbers. The greatest common factor (GCF) of two numbers is the largest factor that divides both numbers. To find the GCF, list all the factors of each number and

2. WHAT’S A MULTIPLE?
A number that can be divided
evenly by another number.
Students will often identify
factors instead of multiples.
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.

3. EXAMPLES
10: 10, 20, 30, 40
15, 30, 45, 60
15:
6: 6, 12, 18, 24
9, 18, 27, 36
9:

4. Write the first 5 multiples of the following.
a.8
b.12
c.11
d.25
e.100

5. LCM – LEAST COMMON MULTIPLE
To find the LCM, list down the multiples in increasing
order.
10:
LCM: 30
10, 20, 30, 40
15, 30, 45, 60
15:
6:
LCM: 18
6, 12, 18, 24
9, 18, 27, 36
9:

6. FIND THE LCM OF EACH NUMBER PAIR.
a. 5, 7
b. 10, 6
c. 4, 9

7. WHAT’S A FACTOR?
A number that can be divided
evenly into another number.
Students will often identify
multiples instead of factors.
Students often miss a factor
when listing them.
Will divide evenly into only some
greater numbers.
There are a limited amount of factors
for each number.
Usually identified in pairs.
Factor

8. FACTORING BY LISTING METHOD
12
1 12
2 6
3 4
32
1 32
2 16
4 8
x
x
x
x
x
x

9. List down all the factors of the following.
a.8
b.12
c. 11
d. 25

11. WHAT’S A PRIME NUMBER?
A number that can be divided
only by itself and 1.
Students often think odd
numbers are prime numbers.
Example: 9
Every number can be divided by a
prime number.
Prime numbers are the foundation of all
numbers.
Prime
Number

12. FIND ALL PRIMES.
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100

13. FACTORING BY PRIME FACTORIZATION

14. FACTORING BY PRIME FACTORIZATION
24

15. FACTORING BY PRIME FACTORIZATION
36

16. FIND THE FACTORS OF THE FOLLOWING.
18 48

17. FACTORIZATION USING REPEATED DIVISION
Find the prime factors of 12.

18. GREATEST COMMON FACTOR
1. List down ALL the factors.
24
18
2. Find the common factors.
3. Find the GREATEST common factor.
18
2
1
9
6
3
6
4
GCF: 6
24
2
1
12
8
3

19. GREATEST COMMON FACTOR
1. List down ALL the factors.
32
20
2. Find the common factors.
3. Find the GREATEST common factor.
20
2
1
10
5
4
GCF: 4
32
2
1
16
8
4