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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
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4-2 Factors and Prime Factorization
Warm UpWarm Up
Lesson PresentationLesson PresentationProblem 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 DayAt 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
Vocabularyfactorprime factorization
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 = 3
6 is divisible by 3 and 2.
4-2 Factors and Prime FactorizationAdditional 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 44 168 You can draw a diagram to illustrate the factor pairs.
Begin listing factors in pairs.
4-2 Factors and Prime FactorizationAdditional 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 FactorizationCheck 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 FactorizationCheck 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 FactorizationAdditional 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•
246 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 FactorizationAdditional 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 FactorizationCheck 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 •
287 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 FactorizationCheck 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
