2-7 prime factorization warm up warm up lesson presentation lesson presentation problem of the day...
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2-7 Prime Factorization
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
2-7 Prime Factorization
Warm UpWrite each number as a product of two whole numbers in as many ways as possible.
1. 6
2. 16
3. 17
4. 36
1 · 6, 2 · 3
1 · 16, 2 · 8, 4 · 4
1 · 17
1 · 36, 2 · 18, 3 · 12, 4 · 9, 6 · 6
2-7 Prime Factorization
Problem of the Day
Nicholas bikes every third day and skates every other day. On April 5 Nicholas biked and skated. When will he do both again?April 11
2-7 Prime Factorization
Prep for MA.7.A.3.2 Add, subtract, multiply, and divide…fractions…Review MA.5.A.2.4
Sunshine State Standards
2-7 Prime Factorization
Vocabulary
prime numbercomposite numberprime factorization
2-7 Prime Factorization
A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself. Three is a prime number because its only factors are 1 and 3.
2-7 Prime Factorization
A composite number is a whole number that has more than two factors. Six is a composite number because it has more than two factors—1, 2, 3, and 6. The number 1 has exactly one factor and is neither prime nor composite.
2-7 Prime Factorization
Tell whether each number is prime or composite.
Additional Example 1: Identifying Prime and Composite Numbers
A. 11
11 is prime.
The factors of 11 are 1 and 11.
B. 16
16 is composite.
The factors of 16 are 1, 2, 4, 8, and 16.
2-7 Prime Factorization
Tell whether each number is prime or composite.
Check It Out: Example 1
A. 14
14 is composite.
The factors of 14 are 1, 2, 7, and 14.
B. 7
7 is prime.
The factors of 7 are 1 and 7.
2-7 Prime Factorization
A composite number can be written as the product of its prime factors. This is called the prime factorization of the number.
You can use a factor tree to find the prime factors of a composite number.
2-7 Prime Factorization
You can write prime factorization by using exponents. The exponent tells how many times to use the base as a factor.
Writing Math
2-7 Prime Factorization
Write the prime factorization of each number.
Additional Example 2A: Using a Factor Tree to Find Prime Factorization
2424
8 · 3
4 · 2 · 3
2 · 2 · 2 · 3
Write 24 as the product oftwo factors.
Continue factoring until allfactors are prime.
The prime factorization of 24 is 2 · 2 · 2 · 3 or 23 · 3.
2-7 Prime Factorization
Write the prime factorization of each number.
Additional Example 2B: Using a Factor Tree to Find Prime Factorization
150150
30 · 5
10 · 3 · 5
2 · 5 · 3 · 5
Write 150 as the productof two factors.
Continue factoring until all factors are prime.
The prime factorization of 150 is 2 · 3 · 5 · 5, or2 · 3 · 52.
2-7 Prime Factorization
Check It Out: Example 2A
Write the prime factorization of each number.
3636
18 · 2
9 · 2 · 2
3 · 3 · 2 · 2
Write 36 as the product oftwo factors.
Continue factoring until allfactors are prime.
The prime factorization of 36 is 2 · 2 · 3 · 3 or 22 · 32.
2-7 Prime Factorization
Check It Out: Example 2B
Write the prime factorization of the number.
9090
45 · 2
9 · 5 · 2
3 · 3 · 5 · 2
Write 90 as the productof two factors.
Continue factoring until all factors are prime.
The prime factorization of 90 is 3 · 3 · 5 · 2, or2 · 32 · 5.
2-7 Prime Factorization
You can also use a step diagram to find a prime factorization. At each step, divide by a prime factor until the quotient is 1.
2-7 Prime Factorization
Write the prime factorization of each number.
Additional Example 3A: Using a Step Diagram to Find Prime Factorization
476
476238119
171
22
717
Divide 476 by 2. Write the quotient below 476.
Keep dividing by a prime number.
Stop when the quotient is 1.
The prime factorization of 476 is 2 · 2 · 7 · 17, or22 · 7 · 17.
2-7 Prime Factorization
Write the prime factorization of the number.
Additional Example 3B: Using a Step Diagram to Find Prime Factorization
275
27555111
5511
Divide 275 by 5. Write the quotientbelow 275.
Stop when the quotient is 1.
The prime factorization of 275 is 5 · 5 · 11, or52 · 11.
2-7 Prime Factorization
Check It Out: Example 3A
Write the prime factorization of each number.
324
32416281
27
1
22
33
Divide 324 by 2. Write the quotient below 324.
Keep dividing by a prime number.
Stop when the quotient is 1.
The prime factorization of 324 is 2 · 2 · 3 · 3 · 3 · 3, or22 · 34.
9333
2-7 Prime Factorization
Check It Out: Example 3B
Write the prime factorization of the number.
325
32565131
5513
Divide 325 by 5. Write the quotientbelow 325.
Stop when the quotient is 1.
The prime factorization of 325 is 5 · 5 · 13, or52 · 13.
2-7 Prime Factorization
There is only one prime factorization for any given composite number. Example 2A began by dividing 476 by 2, the smallest prime factor of 476. Beginning with any prime factor of 476 gives the same result.
476238119
171
22
717
4766834
171
72
217
The prime factorizations are 2 · 2 · 7 · 17 and7 · 2 · 2 · 17, which are the same as 17 · 2 · 2 · 7.
2-7 Prime Factorization
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
2-7 Prime Factorization
Lesson Quiz: Part I
Tell whether each number is prime or composite.
1. 23
2. 39
3. 27
composite
prime
composite
2-7 Prime Factorization
Lesson Quiz: Part II
Write the prime factorization of each number.
4. 27
5. 36
6. 28
7. 132
8. 52
9. 108
22 · 32
33
22 · 7
22 · 3 · 11
22 · 1322 · 33
2-7 Prime Factorization
1. Which of the following is a prime number?
A. 107
B. 108
C. 111
D. 112
Lesson Quiz for Student Response Systems
2-7 Prime Factorization
2. Which of the following is a composite number?
A. 103
B. 107
C. 108
D. 109
Lesson Quiz for Student Response Systems
2-7 Prime Factorization
3. Which of the following is a composite number?
A. 131
B. 133
C. 137
D. 109
Lesson Quiz for Student Response Systems
2-7 Prime Factorization
4. Identify the prime factorization of 125.
A. 52
B. 33
C. 53
D. 73
Lesson Quiz for Student Response Systems
2-7 Prime Factorization
5. Identify the prime factorization of 45.
A. 5 · 9
B. 32 · 5
C. 23 · 5
D. 3 · 15
Lesson Quiz for Student Response Systems