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Number Theory
Prime Numbers and Composite Numbers
Prime Number:
A whole number greater than 1, whose only factors are 1 and
itself.
Composite Number:
A whole number greater than 1 that has more than 2 factors.
7
45
248
67
36
101
23
9
57
Prime Numbers and Composite Numbers
Prime Number:
A whole number greater than 1, whose only factors are 1 and
itself.
Composite Number:
A whole number greater than 1 that has more than 2 factors.
7
45
248
67
36
101
23
9
Prime: 7, 23, 67, 101
Composite: 9, 36, 45, 57, 248
57
Greatest Common Factors in the Real World
Gina is using acorns and leaves to make table centerpieces for a
banquet. She wants each centerpiece to have the same number of
acorns and the same number of leaves. She wants to use all the
leaves and all the acorns.
Gina has the number of acorns and leaves shown below.
What is the greatest number of centerpieces she can make?
How many acorns and leaves can she use for each centerpiece?
42
60
Greatest Common Factors in the Real World
Gina is using acorns and leaves to make table centerpieces for a
banquet. She wants each centerpiece to have the same number of
acorns and the same number of leaves. She wants to use all the
leaves and all the acorns.
Gina has the number of acorns and leaves shown below.
What is the greatest number of centerpieces she can make?
6
How many acorns and leaves can she use for each centerpiece?
7 acorns (7 × 6 = 42), 10 leaves (10 × 6 = 60)
42
60
Greatest Common Factor
The greatest common factor (GCF) is the greatest number
that is a common factor of two or more numbers.
One Way to Find the GCF:
List the factors of each number.
Circle all the factors that the numbers have in common.
The greatest factor is the GCF.
24 and 36
24: 1
36: 1
2
2
3
3
4
4
6
6
8
9
12 24
12 18 36
The GCF is 12.
Find the GCF:
12 and 18
20 and 24
42 and 56
Greatest Common Factor
The greatest common factor (GCF) is the greatest number
that is a common factor of two or more numbers.
One Way to Find the GCF:
List the factors of each number.
Circle all the factors that the numbers have in common.
The greatest factor is the GCF.
24 and 36
24: 1
36: 1
2
2
3
3
4
4
6
6
8
9
12 24
12 18 36
The GCF is 12.
Find the GCF:
12 and 18
6
20 and 24
4
42 and 56
14
Least Common Multiple
The least common multiple (LCM) is the least number that is
a common multiple of two or more numbers.
One Way to Find the LCM:
List some multiples of each number.
Highlight the common multiples in each list.
The least multiple (the first common multiple) in both lists is the LCM.
8 and 12
8: 8 16 24 32 40 48 56
12: 12 24 36 48 60
The LCM is 24.
Find the LCM:
9 and 15
18 and 27
10 and 12
Least Common Multiple
The least common multiple (LCM) is the least number that is
a common multiple of two or more numbers.
One Way to Find the LCM:
List some multiples of each number.
Highlight the common multiples in each list.
The least multiple (the first common multiple) in both lists is the LCM.
8 and 12
8: 8 16 24 32 40 48 56
12: 12 24 36 48 60
The LCM is 24.
Find the LCM:
9 and 15
45
18 and 27
54
10 and 12
60
Prime Factorization
Prime Factorization is the expression of a composite number
as the product of its prime factors.
Make a Factor Tree
Divide by Prime Factors
Start with any two factors.
Start with the number.
Keep factoring the factors until
all the factors are prime.
Divide by prime factors until all
factors are prime.
Write in exponential form.
Write in exponential form.
6
54
×
9
×
3×3
×
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
2
3
54 = 2 × 3 × 3 × 3 = 2 × 33
100 = 2 × 2 × 5 × 5 = 22 × 52
Find the prime factorization of each number.
36
45
120
Prime Factorization
Prime Factorization is the expression of a composite number
as the product of its prime factors.
Make a Factor Tree
Divide by Prime Factors
Start with any two factors.
Start with the number.
Keep factoring the factors until
all the factors are prime.
Divide by prime factors until all
factors are prime.
Write in exponential form.
Write in exponential form.
6
54
×
9
×
3×3
×
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
2
3
54 = 2 × 3 × 3 × 3 = 2 × 33
100 = 2 × 2 × 5 × 5 = 22 × 52
Find the prime factorization of each number.
36
22 × 32
45
32 × 5
120 23 × 3 × 5
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