4-2 factors and prime factorization warm up warm up lesson presentation lesson presentation problem...
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4-2 Factors and Prime Factorization
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
4-2 Factors and Prime Factorization
Warm UpIdentify each number as prime or composite.
1. 19 2. 82
3. 57 4. 85
5. 101 6. 121
prime composite
composite composite
compositeprime
4-2 Factors and Prime Factorization
Problem of the Day
At the first train stop, 7 people disembarked. At the second stop, 8 people disembarked. At the fourth stop, the last 6 people disembarked. If there were 28 people on the train before the first stop, how many people left at the third stop?
7 people left at the third stop
4-2 Factors and Prime Factorization
Prep for MA.6.A.5.1 Use equivalent forms of fractions, decimals…to solve problems.
Also Review of MA.5.A.2.4
Sunshine State Standards
4-2 Factors and Prime Factorization
Whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors.
2 3 6=
FactorsProduct
26 3÷ =
6 ÷2 = 36 is divisible by 3 and 2.
4-2 Factors and Prime Factorization
Additional Example 1A: Finding Factors
List all of the factors of the number 16.A. 16
16 = 1 • 1616 = 2 • 8
1 is a factor.2 is a factor.
16 = 4 • 43 is not a factor.4 is a factor.5 is not a factor.6 is not a factor.7 is not a factor.
16 = 8 • 2 8 and 2 have already been listed, so stop here.
The factors of 16 are 1, 2, 4, 8, and 16.
1 2 44 168You can draw a diagram to illustrate the factor pairs.
Begin listing factors in pairs.
4-2 Factors and Prime Factorization
Additional Example 1B: Finding Factors
List all of the factors of the number 19.
B. 19
19 = 1 • 19 Begin listing factors in pairs. 19 is not divisible by any other whole numbers.
The factors of 19 are 1 and 19.
4-2 Factors and Prime Factorization
Check It Out: Example 1A
List all of the factors of the number 12.
A. 12
12 = 1 • 1212 = 2 • 6
1 is a factor.2 is a factor.3 is a factor.4 and 3 have already been listed, so stop here.
12 = 4 • 3
1 2 43 126
The factors of 12 are 1, 2, 3, 4, 6, and 12
12 = 3 • 4
You can draw a diagram to illustrate the factor pairs.
Begin listing factors in pairs.
4-2 Factors and Prime Factorization
Check It Out: Example 1B
List all of the factors of the number 11.
B. 11
11 = 1 • 11 Begin listing factors in pairs. 11 is not divisible by any other whole numbers.
The factors of 11 are 1 and 11.
4-2 Factors and Prime Factorization
You can use factors to write a number in different ways.
Factorization of 12
2 • 61 • 12 3 • 4 3 • 2 • 2
The prime factorization of a number is the number written as the product of its prime factors.
Notice that these factors are all prime.
4-2 Factors and Prime Factorization
You can use exponents to write prime factorizations. Remember that an exponent tells you how many times the base is a factor.
Helpful Hint
4-2 Factors and Prime Factorization
Additional Example 2A: Writing Prime Factorizations
Method 1: Use a factor tree.
Choose any two factors of 24 to begin. Keep finding factors until each branch ends at a prime factor.
24
2 12•
6
2
2 •
3•
24
6 4•
3 2 2 2
24 = 2 • 2 • 2 • 3
24 = 3 • 2 • 2 • 2
The prime factorization of 24 is 2 • 2 • 2 • 3, or 23 • 3.
• •
Write the prime factorization of 24.
4-2 Factors and Prime Factorization
Additional Example 2B: Writing Prime Factorizations
Method 2: Use a ladder diagram.
Choose a prime factor of 45 to begin. Keep dividing by prime factors until the quotient is 1.
3 45
3
1
15
55
45 = 3 • 3 • 5
5 45
3
1
9
3 3
45 = 5 • 3 • 3
The prime factorization of 45 is 3 • 3 • 5 or 32 • 5 .
Write the prime factorization of 45.
4-2 Factors and Prime Factorization
In Example 2, notice that the prime factors may be written in a different order, but they are still the same factors. Except for changes in the order, there is only one way to write the prime factorization of a number.
4-2 Factors and Prime Factorization
Check It Out: Example 2A
Write the prime factorization of 28.
Method 1: Use a factor tree.
Choose any two factors of 28 to begin. Keep finding factors until each branch ends at a prime factor.
28
2 14•
72 •
28
7 4•
2 2
28 = 2 • 2 • 7 28 = 7 • 2 • 2
The prime factorization of 28 is 2 • 2 • 7, or 22 • 7 .
•
4-2 Factors and Prime Factorization
Check It Out: Example 2B
Write the prime factorization of 36.
Method 2: Use a ladder diagram.
Choose a prime factor of 36 to begin. Keep dividing by prime factors until the quotient is 1.
3 36
2
1
12
62
36 = 3 • 2 • 2 • 3
The prime factorization of 36 is 3 • 2 • 2 • 3, or 32 • 23.
3 36
3
1
12
2 4
36 = 3 • 3 • 2 • 2
33 2 2
4-2 Factors and Prime Factorization
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
4-2 Factors and Prime Factorization
Lesson Quiz
List all the factors of each number.
1. 22
2. 40
3. 51
1, 2, 4, 5, 8, 10, 20, 40
1, 2, 11, 22
1, 3, 17, 51
Write the prime factorization of each number.
4. 32
5. 120
25
23 3 5
4-2 Factors and Prime Factorization
1. Which of the following lists all the factors of 33?
A. 1, 2, 11, 22
B. 2, 22
C. 3, 11
D. 1, 3, 11, 33
Lesson Quiz for Student Response Systems
4-2 Factors and Prime Factorization
2. Which of the following lists all the factors of 30?
A. 1, 2, 3, 4, 5, 6, 7, 30
B. 1, 2, 3, 5, 6, 10, 15, 30
C. 5, 7, 10, 12, 15
D. 4, 8, 12, 13, 17
Lesson Quiz for Student Response Systems
4-2 Factors and Prime Factorization
3. Which of the following lists all the factors of 14?
A. 1, 4, 14
B. 1, 7, 14
C. 1, 2, 7, 14
D. 1, 2, 4, 14
Lesson Quiz for Student Response Systems
4-2 Factors and Prime Factorization
4. Identify the prime factorization of 625.
A. 34
B. 33 5
C. 3 53
D. 54
Lesson Quiz for Student Response Systems