1. Number Theory

2. Prime Numbers and Composite Numbers
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 36 9
101 67 57 23

3. Prime Numbers and Composite Numbers
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 36 9
101 67 57 23
Prime: 7, 23, 67, 101
Composite: 9, 36, 45, 57, 248

4. 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

5. 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 6
7 acorns (7 × 6 = 42), 10 leaves (10 × 6 = 60)

6. 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:
36:
The GCF is 12. 2 3 4 6 8 9 12 24 18
Find the GCF:
12 and 18
20 and 24
42 and 56 36 1

7. 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:
36:
The GCF is 12. 2 3 4 6 8 9 12 24 18
Find the GCF:
12 and 18
20 and 24
42 and 56 14 36 1

8. Least Common Multiple 8 and 12 The LCM is 24. 8: 12: 8 12 16 24 36 32
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:
12:
The LCM is 24. 8 12 16 24 36 32 48 40 60
48 56
Find the LCM:
9 and 15
18 and 27
10 and 12

9. Least Common Multiple 8 and 12 The LCM is 24. 8: 12: 8 12 16 24 36 32
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:
12:
The LCM is 24. 8 12 16 24 36 32 48 40 60
48 56
Find the LCM:
9 and 15
18 and 27
10 and 12 45 54

10. Find the prime factorization of each number. Divide by Prime Factors
Prime Factorization is the expression of a composite number as the product of its prime factors.
Find the prime factorization of each number. 36 45
120
Make a Factor Tree
Start with any two factors.
Keep factoring the factors until all the factors are prime.
Write in exponential form.
Divide by Prime Factors
Start with the number.
Divide by prime factors until all factors are prime.
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
100 = 2 × 2 × 5 × 5 = 22 × 52 54 6 9 3 2 ×
54 = 2 × 3 × 3 × 3 = 2 × 33

11. Find the prime factorization of each number. Divide by Prime Factors
Prime Factorization is the expression of a composite number as the product of its prime factors.
Find the prime factorization of each number. 36 45
120
22 × 32
32 × 5
23 × 3 × 5
Make a Factor Tree
Start with any two factors.
Keep factoring the factors until all the factors are prime.
Write in exponential form.
Divide by Prime Factors
Start with the number.
Divide by prime factors until all factors are prime.
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
100 = 2 × 2 × 5 × 5 = 22 × 52 54 6 9 3 2 ×
54 = 2 × 3 × 3 × 3 = 2 × 33

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