Factors and Divisibility - Quia

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Factors and Divisibility

R 7-1

One number is divisible by another number when the quotient is a whole number and the remainder is zero. You can use the divisibility rules to help you find factors of a number.

Example 1

Is 9 a factor of 117?

If 117 is divisible by 9, then 9 is a factor of 117.

Use the divisibility rule for 9: the sum of the digits is 1 1 7 9. 9 is divisible by 9, so 117 is divisible by 9.

Divisible by 2 3

4 5 6 9 10

Divisibility Rules Rule

The number is even. The sum of the digits is divisible by 3. The number formed by the tens and ones digits is divisible by 4. The ones digit is 0 or 5. The number is divisible by 2 and 3. The sum of the digits is divisible by 9. The ones digit is 0.

Example 2

List all the factors of 32. Try 1, then 2, then 3, and so on.

The factors of 32 are 1, 2, 4, 8, 16, and 32.

Try: Is it a factor?

1 Yes, 1 32 32 2 Yes, 2 16 32 3 No. 4 Yes, 4 8 32 5 No. 6 No. 7 No. 8 Yes, 8 4 32

Factors: 1, 32 2, 16 4, 8

8, 4

Mental Math Tell if each number is divisible by 2, 3, 4, 5, 6, 9, or 10.

1. 39

2. 120

3. 56

4. 4,731

5. 356

6. 425

7. 1,240

8. 331

9. 744

10. 123

? Scott Foresman, Gr. 5 (209)

Use with Chapter 7, Lesson 1.

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Factors and Divisibility

Fill in the chart. Write if each number is divisible by 2, 3, 4, 5, 6, 9, or 10.

H 7-1

Divisible by

2

3

4

5

6

9

10

1.

24

2.

65

3.

79

4.

60

5.

45

6.

423

7.

5,170

8.

7,536

9.

9,000

10.

2,222

11.

31,770

12.

501,264

List all the factors of each number. 13. 33 15. 53

14. 74 16. 94

17. Math Reasoning If a number is divisible by 12, is it also divisible by 2, 3, 4, and 6?

Test Prep Circle the correct letter for each answer.

18. Which number is divisible by 2, 3, 4, 5, 6, 9 and 10?

F 1,422

G 9,002

H 45,360

J 64,860

? Scott Foresman, Gr. 5 (210)

Use with Chapter 7, Lesson 1.

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Prime Factorization

R 7-2

A whole number greater than 1 is either a prime number or a composite number. A prime number has exactly two factors, 1 and the number itself. A composite number has more than two factors.

Example 1

List the numbers from 50 to 60. Which numbers are prime?

50 51 52 53 54 55 56 57 58 59 60

Cross out all the numbers that are divisible by 2 since they are not prime. Cross out all the numbers divisible by 3 since they are not prime. Continue until only prime numbers remain. The prime numbers from 50 through 60 are 53, 57, and 59.

Example 2

Use a factor tree to find the factorization of 24. Write 24 as a product of two factors. Then write each factor that is not prime as a product.

24

Write 24 as a product. 2 is prime, 12 is not prime.

2

12

Write 12 as a product.

2

2

6

Write 6 as a product.

2

2

2

3

2 and 3 are prime.

If a factor appears more than once, exponents can be used. 24 2 2 2 3 23 3

Complete each factor tree. Then write the prime factorization using exponents if possible.

1.

9

3.

16

32

2.

15

15

x

24

? Scott Foresman, Gr. 5 (212)

Use with Chapter 7, Lesson 2.

Name _____________________________________________________________________________________________________

Prime Factorization

H 7-2

Complete each factor tree. Then write the prime factorization, using exponents if possible.

1.

42

2.

56

6

7

42

56

Write the prime factorization of each composite number, using exponents when possible. If a number is prime, write prime.

3. 55

4. 29

5. 28

6. 120

7. 72 11. 80

8. 64 12. 49

9. 45 13. 13

10. 36 14. 83

15. 30 19. 59

16. 31 20. 99

17. 88 21. 57

18. 77 22. 60

Test Prep Circle the correct letter for each answer.

23. Which is the prime factorization of 72? A 2 2 2 3 B 22 3 3

24. Which is the prime factorization of 294?

F 2 147

G 2 21 7

C 22 33 H 2 32 7

? Scott Foresman, Gr. 5 (213)

D 23 32 J 2 3 72

Use with Chapter 7, Lesson 2.

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Common Factors and GCF

R 7-3

You can use what you know about divisibility and fact families to help you find the greatest common factor.

Find the greatest common factor of 9 and 12. List all of the factors of each number. Remember to use divisibility rules.

Factors of 9: 1, 3, 9

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

Then list the common factors, those numbers that are in both lists.

Common factors: 1, 3

The largest number in this list is 3. The greatest common factor (GCF) of 9 and 12 is 3. The greatest common factor is sometimes called the greatest common divisor (GCD).

The common factors of 9 and 12 are 1 and 3.

The greatest common factor (GCF) of 9 and 12 is 3. The greatest number that can be in each group is 3.

List the factors of each number. Then find the GCF for each set of numbers.

1. 15

10

factors:

factors:

GCF:

2. 24 factors:

18 factors:

GCF:

3. 45 factors:

27 factors:

GCF:

? Scott Foresman, Gr. 5 (215)

Use with Chapter 7, Lesson 3.

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Common Factors and GCF

List the factors of each number. Then find the GCF of each set of numbers

H 7-3

1. 25, 34 25 34 GCF

2. 16, 20 16 20 GCF

3. 16, 28, 48 16 28 48

4. 20, 35, 70 20 35 70

GCF

5. Draw a Venn diagram to show the factors of 24 and 30. What are the common factors? What is the greatest common factor?

GCF

6. A toy shop has 40 red marbles and 56 yellow marbles lying loose in a bin. The shop owner wants to package them so that there are the same number of each per each bag.

How many bags will there be?

How many red marbles will be in each bag?

How many yellow marbles?

Test Prep Circle the correct letter for each answer.

7. Which is the GCF for 12, 20, and 36?

A 12

B4

C 36

D9

8. Which is the GCF for 5, 13, and 26?

F5

G2

H 13

J1

? Scott Foresman, Gr. 5 (216)

Use with Chapter 7, Lesson 3.

Name _____________________________________________________________________________________________________

Common Multiples and LCM

R 7-4

A multiple of a whole number is the product of that number and any other whole number. 44 is a multiple of 4 because 4 11 44. 44 is also a multiple of 11. Common multiples of numbers are multiples that are the same for each number.

Multiples of 4: 4, 8, 16, 20, 24, 28, 32, 36, 40 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 Common multiples: 20, 40, . . . LCM: 20 Some common multiples of 4 and 8 are 8, 16, 24, and 32. The least common multiple (LCM) is 8.

List the first ten multiples of each number.

1. 2

2. 3

3. 5

4. 7

5. 9

Using the multiples above, list the common multiples shown for each set of numbers. Then circle the LCM.

6. 2, 7

7. 2, 3

8. 9, 7

9. 3, 5

List the first ten multiples of each number. Then find the LCM of each number.

10. 5, 6 5

6 11. 3, 5

3

LCM

5

LCM

? Scott Foresman, Gr. 5 (218)

Use with Chapter 7, Lesson 4.

Name _____________________________________________________________________________________________________

Common Multiples and LCM

H 7-4

List the first ten multiples of each number. Then find the LCM of the numbers. 1. 4, 5

4 5 LCM

2. 8, 9

8

9

LCM

3. 3, 5, 6

3

5

6

LCM

4. Laurie set up the household task schedule at the right. If she begins her schedule on the first day of each month, on which days will she have two tasks to do?

Monthly Schedule

Task

Frequency

5. On which days will she have 3 tasks?

Take out trash Water plants

Every 2 days Every 4 days

Clean room

Every 7 days

Test Prep Circle the correct letter for each answer.

6. Which is the least common multiple of 12 and 18?

A 12

B 18

C6

D 36

7. Which is the least common multiple of 6, 8, and 12?

F 12

G 24

H 36

J 48

? Scott Foresman, Gr. 5 (219)

Use with Chapter 7, Lesson 4.

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