5 2 prime factorization weebly

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Reteaching 5-2

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Name

Prime Factorization

Reteaching

5-2

A prime number has exactly two factors, 1 and itself.

Example: 17 is prime. Its factors are 1 and 17.

A composite number has more than two factors.

Example: 10 is composite. Its factors are 1, 2, 5, and 10.

One way to find the prime factors of a composite number is to divide by prime numbers.

84 ? 2 = 42 42 ? 2 = 21 21 ? 3 = 7 7 ? 7 = 1

84 is even. Divide by 2. Divide by 2 until the quotient is odd. 3 is a prime factor of 21, divide by 3. 7 is prime. You have found the prime factors.

Write the prime factors from least to greatest: 84 = 2 ? 2 ? 3 ? 7. Then write the factors in exponential form: 22 ? 3 ? 7.

For 1 through 12, if a number is prime, write prime. If the number is composite, write the

prime factorization.

1. 28 22 ? 7

2. 36 22 ? 32

3. 29 Prime

5. 55 5 ? 11 7. 84 22 ?3 ? 7 9. 75 52 ? 3 11. 45 32 ?5

4. 70 2 ? 5 ? 7 6. 81 34 8. 99 32 ? 11

10. 43 Prime 26

12. 64

13. Writing to Explain Explain how you can check to see if your prime factorization is

correct.

Sample answer: Multiply the prime numbers to

see if you get the original number.

14. Strategy Practice How can you tell that 342 is divisible by 3?

Sample answer: The sum of the digits is divisible by 3.

34 Topic 5

Practice 5-2

Name

Prime Factorization

Practice

5-2

For 1 through 10 if the number is prime, write prime. If the number is composite, write the

prime factorization.

1. 24 23 ? 3

2. 43 Prime

3. 51 3 ? 17

5. 61 Prime 7. 144 24 ? 32 9. 270 2 ? 33 ? 5

4. 66 6. 96 8. 243 10. 124

2 ? 3 ? 11 25 ? 3 35 22 ? 31

11. Writing to Explain Find the first ten prime numbers. Tell how you do it.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29; Sample answer: Use divisibility rules to check that no lesser number can be divided into the number you 12. Reasoning How many even prime numbers are there? are testing.

A 0

B 1

C 2

D 3

13. Critical Thinking Which answer completes the sentence below?

The number 1 is

.

A prime. B composite. C neither prime nor composite. D both prime and composite.

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Topic 5 35

Reteaching 5-3

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Name

Greatest Common Factor

Reteaching

5-3

The greatest number that divides into two numbers is the greatest common factor (GCF) of the two numbers. Here are two ways to find the GCF of 12 and 40.

List the Factors

Use Prime Factorization

Step 1: List the factors of each number.

12: 1, 2, 3, 4, 6, 12

40: 1, 2, 4, 5, 8, 10, 20, 40

Step 2: Circle the factors that are common to both numbers.

12: 1, 2, 3, 4, 6, 12

40: 1, 2, 4, 5, 8, 10, 20, 40

Step 3: Choose the greatest factor that is common to both numbers. Both 2 and 4 are common factors, but 4 is greater.

The GCF is 4.

Step 1: Write the prime factorization of each number. 12: 2 ? 2 ? 3 40: 2 ? 2 ? 2 ? 5 Step 2: Circle the prime factors that the numbers have in common. 12: 2 ? 2 ? 3 40: 2 ? 2 ? 2 ? 5 Step 3: Multiply the common factors. 2 ? 2 = 4 The GCF is 4.

Find the GCF for each set of numbers.

1. 10, 70 10

4 2. 4, 20

9 4. 18, 63

6 5. 36, 42

6 3. 18, 24 6. 14, 28 14

7. Number Sense Name two numbers that have a greatest common factor of 8.

Sample answer: 16 and 24

8. Geometry Al's garden is 18 feet long and 30 feet wide. He wants to put fence posts the same distance apart along both the length and width of the fence. What is the greatest distance apart he can put the fence posts?

6 feet

40 Topic 5

Name

Greatest Common Factor

Practice

5-3

Find the GCF for each set of numbers.

1. 12, 48 12

4 2. 20, 24

4 4. 24, 100

2 5. 18, 130

3. 21, 84 21 5 6. 200, 205

7. Number Sense Name three pairs of numbers that have 5 as their greatest common factor. Use each number only once in your answer.

Sample answer: 5, 10; 25, 30; 50, 55

Practice 5-3

8. The bake-sale committee divided each type of item evenly onto plates, so that every plate contained only one type of item and every plate had exactly the same number of items with no leftovers. What is the maximum number of items that could have been placed on each plate?

12

Bake Sale Donations

Muffins

96

Bread sticks 48

Rolls

84

9. Using this system, how many plates of rolls could the

bake-sale committee make?

7

10. Using this system, how many plates of muffins could the bake-sale committee make?

8

11. Which of the following pairs of numbers is correctly listed with its greatest common factor?

A 20, 24; GCF: 4 B 50, 100; GCF: 25 C 4, 6; GCF: 24 D 15, 20; GCF: 10 12. Writing to Explain Explain one method of finding the greatest common factor of 48 and 84.

Sample answer: You can use prime factorization to find the GCF of 48 and 84 by multiplying their common prime factors: 2 2 3 12.

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Topic 5 41

Name

Understanding Fractions

Reteaching

5-4

Fractions are used to show part of a set. Fractions are used to show part of 1 whole.

The fraction of the shapes that are stars can be written as:

_____N_u_m__b_e_r__o_f _s_t_a_rs_____ Total number of shapes

=

_3__ 7

0

1

The length between 0 and 1 is divided into 4 equal sections. The fraction for the shaded section can be written as:

_N__u_m__b_e_r_o_f__s_h_a_d_e_d__s_e_c_t_io__n_s_ = _3__ Total number of sections 4

Write the fraction that represents the shaded portion.

1.

2.

Reteaching 5-4

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_N__u_m__b_e_r_o_f__s_h_a_d_e_d__p_a_r_t_s_ = _4__ Total number of parts

9;

_ 4

9

3.

0

1

_ 7

8

Draw models of fractions.

5. Draw a set and shade _25.

Sample answer

_N__u_m__b_e_r_o_f__s_h_a_d_e_d__c_ir_c_l_e_s_ = ___ Total number of circles

_5_

11

4 .

0

_4_

10

Centimeters 1

6. Draw a whole and shade _34.

Sample answer

7.

Number Sense

_ 2

If

you

shade

_ 1

3

of a set,

what fraction of

the

set is not shaded?

3

46 Topic 5

Practice 5-4

Name

Understanding Fractions

Write the fraction that represents the shaded portion.

1.

2.

_ 3

_ 1

6

4

Practice

5-4

3.

_ 6

9

Draw models of fractions.

5.

Draw a set to

Sample

raepnressewnt e_140_.r

4.

0

_2_

10

Centimeters 1

6.

Draw a number line to represent

Sample answer

_16.

0

1

7. Write a Problem Write a fraction problem that can be solved using this model.

Sample answer;

What fraction of the

arrows

are

pointing

up?

;

_ 2

8

or

_ 1

4

8. Writing to Explain Sharon drew this drawing to show _35. Is her drawing correct? Explain why or why not.

It is not correct because all of the sections are not the same size.

9. Estimation Which is the best estimate of how full the cup is?

A

_ 3

4

full

B

_ 1

2

full

C

_ 1

3

full

D

_ 1

8

full

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Topic 5 47