Section 2.1 – Factors and Multiples · only whole number that is neither prime nor composite. Table of Prime Numbers Less Than 1,000 ... 8 - : - : prime factorization × . × 1

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Section 2.1 – Factors and Multiples

When you want to prepare a salad, you select certain ingredients (lettuce,

tomatoes, broccoli, celery, olives, etc.) to give the salad a specific taste. You can

think of the salad as the final result, or product, of combining the ingredients. In

general, the order in which you combine these ingredients does not affect the

taste and nutritional value of the salad.

We saw in the previous chapter that whenever we multiply two or more whole

numbers, we get another whole number as the final result. For example,

× × =

We can think of the numbers 17, 3 and 11 as the “ingredients” that multiplied

together make up the “salad,” or final result of 561. In mathematics, the

ingredients are called factors and we call the salad a product or multiple. Thus,

we say that the whole numbers 17, 3 and 11 are the factors that multiplied

together give the product 561. The number 561 is a multiple of 17, 3, and 11,

which means that 561 is divisible by 17, 3, and 11 because $561 can be evenly

divided among 17 people, among 3 people or among 11 people without resorting

to cents.

In the following equation, name the factors and the multiple.

× × × = ,

Example 2.1.1

Answer: The numbers 13, 47, 5 and 241 are factors of the product 736,255,

whereas the product 736,255 is a multiple of 13, 47, 5 and 241. This means that

736,255 is divisible by 13, 47, 5 and 241. You can think of 736,255 as being the

“salad” and the numbers 13, 47, 5 and 241 the “ingredients” that multiplied

together give 736,255.


In the following equation, name the factors and the product.

× × × = ,

Note: The order in which you multiply the factors doesn’t affect the final product

because multiplication is commutative.

For example: 8 × 5 × 2 = 5 × 8 × 2 = 2 × 8 × 5 = 80

Whenever we can write a whole number as the product of a set of whole

numbers (its factors), we say that the product is divisible by those numbers. That

is, any whole number is divisible by its factors.

Since 7 × 8 = 56, we know that 56 is divisible by 7 and that 56 is divisible by 8.

Therefore, 56 is a multiple of 7 and 8, while 7 and 8 are factors of 56. The

complete list of factors of 56 is 1, 2, 4, 14, 28 and 56.

8

7 5 6

- 5 6

0

7

8 5 6

- 5 6

0

Example 2.1.2

Answer: The numbers 6, 4, 23 and 11 are factors of 6,072, whereas the number

6,072 is a multiple of 6, 4, 23 and 11.

Example 2.1.3

Since 7x8=56, then 56 is the product and 7

and 8 are factors of 56. Notice that

whenever we divide a product by one of its

factors, the quotient is also a factor and the

remainder is always zero.

factors multiple

factors multiple


Since 2 × 28 = 56, we know that 56 is divisible by 2 and that 56 is divisible by 28.

Therefore, 56 is a multiple of 2 and 28, while 2 and 28 are factors of 56.

Note: 1 is a factor of any whole number because 1 × = . This also means

that any whole number is divisible by 1.

For example,

1 is a factor of 17 since 1 × 17 = 17. Therefore, 17 is divisible by 1.

1 is a factor of 5,788 since 1 × 5,788 = 5,788. Therefore, 5,788 is divisible by 1.

Let’s check that the remainder is zero:

2 8

2 5 6

- 5 6

0

2

2 8 5 6

- 5 6

0

1 7

1 1 7

- 1

0 7

- 7

0

5 7 8 8

1 5 7 8 8

- 5

0 7

- 7

0 8

- 8

0 8

- 8

0

Factor

Factor Multiple

- :

0

Example 2.1.4

Since 2x28=56, then 56 is the product and

2 and 28 its factors. Notice that whenever

we divide a product by one of its factors,

the quotient is also a factor and the

remainder is always zero.

remainder

factors

multiple factors

multiple


The following are special whole numbers that you should become familiar with:

Number Definition Examples

Even Any number that is divisible by 2. It has 2

as a factor.

0,2,4,6,8,10,12,14,16, …

Odd Any number that is not divisible by 2. It

does not have 2 as a factor.

1,3,5,7,9,11,13,15,17,…

Prime Any whole number that has exactly 2

different factors: 1 and the number itself.

2,3,5,7,11,13,17,19,23,...

Composite Any whole number greater than 1 that is

not a prime number.

4,6,8,9,10,12,14,15,16,…

Note: The number 1 is not a prime number because it has only one factor (itself),

since 1 × 1 = 1. Moreover, 1 is not a composite number either. In fact, 1 is the

only whole number that is neither prime nor composite.

Table of Prime Numbers Less Than 1,000

2 3 5 7 11 13 17 19 23

29 31 37 41 43 47 53 59 61 67

71 73 79 83 89 97 101 103 107 109

113 127 131 137 139 149 151 157 163 167

173 179 181 191 193 197 199 211 223 227

229 233 239 241 251 257 263 269 271 277

281 283 293 307 311 313 317 331 337 347

349 353 359 367 373 379 383 389 397 401

409 419 421 431 433 439 443 449 457 461

463 467 479 487 491 499 503 509 521 523

541 547 557 563 569 571 577 587 593 599

601 607 613 617 619 631 641 643 647 653

659 661 673 677 683 691 701 709 719 727

733 739 743 751 757 761 769 773 787 797

809 811 821 823 827 829 839 853 857 859

863 877 881 883 887 907 911 919 929 937

941 947 953 967 971 977 983 991 997


Make a table of all the factors of 24.

The number at the top of the table shown in blue (24) is a multiple of all the

numbers in green. Conversely, the numbers in green are factors of 24.

In the table above, we see that 24 is a factor and multiple of itself. In fact, any

whole number is a factor and multiple of itself because we can always write

1 × = .


Example 2.1.5

Answer:

24

1 24

2 12

3 8

4 6

1, 2, 3, 4, 6, 8, 12 and 24

are factors of 24 because

1x24=24

2x12=24

3x8=24

4x6=24

Example 2.1.6

Answer:

120

1 120

2 60

3 40

4 30

5 24

6 20

8 15

10 12

1, 2, 3, 4, 5, 6, 8, 10, 12,

15, 20, 24, 30, 40, 60 and

120 are factors of 120

because

1x120=120

2x60=120

3x40=120

4x30=120

5x24=120

6x20=120

8x15=120

10x12=120



The number 700 at the top of the table (shown in blue) is a multiple of all the

numbers in green. Similarly, the numbers in green are factors of 700.

Please seek help from your instructor if you have difficulty understanding the

difference between a multiple and a factor.

Here is an instructional video on what a multiple of a number is:

http://www.youtube.com/watch?v=vbNeXLvqM90

Example 2.1.7

Answer:

700

1 700

2 350

4 175

5 140

7 100

10 70

14 50

20 35

25 28

1, 2, 4, 5, 7, 10, 14, 20,

25, 28, 35, 50, 70, 100,

140, 175, 350 and 700 are

factors of 700 because

1x700=700

2x350=700

4x175=700

5x140=700

7x100=700

10x70=700

14x50=700

20x35=700

25x28=700


1. Is 4 a factor of 216? Explain why or why not.


3. Given that 5 × 13 × 17 = 1105 state whether the following statements are

true or false:

A. 5 is a factor of 1105.

B. 17 is a factor of 1105.

C. 1105 is a factor of 13.

D. 1105 is a multiple of 17.

E. 1105 is a multiple of 5.

F. 1105 is divisible by 13.

G. 5 is a factor of 13.

4. Is 200 a multiple of 10?





9. Write a table of all the factors of 90.


11. True or false:

a. 7 is a prime number.

b. 90 is a prime number.

Classwork 2.1


c. 63 is a composite number.

d. 15 is a prime number.

e. 41 is a composite number.

f. 28 is a composite number.

g. 9 is a prime number.

h. 1 is a prime number.

i. 1 is a composite number.

j. 945 is a composite number.

k. 121 is a prime number.

l. 200 is a composite number.


13. True or false:


b. 70 is a composite number.




f. 45 is a prime number.



i. 3,250 is a composite number.




l. 1,011 is a prime number.

14. T/F _____ 90 is divisible by 10.


16. T/F _____ 7,326 is divisible by 3.






4 216 4 × 54 = 216 ( 216 4 0 ).

17 91 91 17 .

CW 2.1 Solutions:

1.

2.

3. A. True B. True C. False D. True E. True F. True G. False

4. Yes 5. Yes 6. No 7. Yes 8. No

9. 10.

11. a. True b. False c. True d. False e. False f. True g. False h. False i. False

j. True k. False l. True

12.

13. a. True b. True c. True d. False e. True f. False g. False h. False i. True j. True

k. False l. False

14. T 15. F 16. T 17. T 18. F 19. T 20. F

90

1 90

2 45

3 30

5 18

6 15

9 10

64

1 64

2 32

4 16

8 8

30

1 30

2 15

3 10

5 6




3. Given that 8 × 19 = 152 state whether the following statements are true or

false:

A. 8 is a factor of 152.

B. 19 is a factor of 152.

C. 152 is a multiple of 8.

D. 152 is divisible by 19.

E. 152 is a multiple of 19.

F. 152 is a factor of 8.

G. 8 is a factor of 19.

4. Is 34,590 a multiple of 5?

5. Is 400 a multiple of 1,200?

6. Is 6 a factor of 30?

7. Is 144 divisible by 8?




11. True or false:


b. 29 is a prime number.

Homework 2.1




e. 11 is a prime number.


g. 450 is a composite number.





l. 27 is a prime number.


13. True or false:


b. 63 is a composite number.






h. 8,674 is a prime number.





l. 999 is a prime number.









9 325 325 9 .

12 240 12 × 20 = 240 ( 240 12 ).

HW 2.1 Solutions:

1.

2.

3. A. True B. True C. True D. True E. True F. False G. False

4. Yes 5. No 6. Yes 7. Yes 8. No

9. 10.

11. a. False b. True c. False d. False e. True f. False g. True h. True i. True

j. True k. False l. False

12.

13. a. False b. True c. False d. False e. True f. False g. False h. False i. True j. False

k. True l. False

14. T 15. F 16. T 17. F 18. T 19. T 20. F

44

1 44

2 22

4 11

150

1 150

2 75

3 50

5 30

6 25

10 15

Answer:

100

1 100

2 50

4 25

5 20

10 10


Section 2.2 – Rules of Divisibility

In the previous section, we learned what it means for a number to be

divisible by another number. In particular, if we have × = , this means that

and are both factors of . This also means if we divide by or by , the

remainder will be zero. Therefore, × = means that is divisible by and

that is divisible by . For example, since 15 × 2 = 30, both 15 and 2 are factors

of 30. This means that 30 is divisible by 15 and that 30 is divisible by 2. This means

that we get a zero remainder when we divide 30 by 2 and a zero reminder when

we divide 30 by 15. Checking that the remainder is zero is a way to test

divisibility.

Unfortunately, the long division process might be time consuming in some

instances, depending on the numbers that are being divided. Therefore, it is

advantageous to memorize the following divisibility rules of whole numbers and

apply them as appropriate. There are many divisibility rules, but only the most

basic and easy to remember are presented in this table.

Divisible

by Condition Examples

1 All whole numbers are divisible by 1. 0,1,2,3,4,5,6,7,8,9,10,11,12,13,…

2 If the number is even. 0,2,4,6,8,10,12,14,16,18,20,22,…

3 If the sum of the digits is divisible by 3. 0,3,6,9,12,15,18,21,24,27,30,33,…

4 If the 2 rightmost digits are divisible by 4. 0,4,8,12,16,20,24,28,32,36,40,44,…

5 If the number ends with a 5 or 0. 0,5,10,15,20,25,30,35,40,45,50,...

6 If the number is divisible by 2 and by 3. 0,6,12,18,24,30,36,42,48,54,60,…

9 If the sum of the digits is divisible by 9. 0,9,18,27,36,45,54,63,72,81,90,…

10 If the number ends with 0 0,10,20,30,40,50,60,70,80,90,100,…

2

1 5 3 0

- 3 0

0

1 5

2 3 0

- 2

1 0

1 0

0

F

F M - :

0 remainder

factors

multiple

factors

multiple


Determine whether the number 345,726 is divisible by 1, 2, 3, 5 or 6.

Determine whether the number 68,970 is divisible by 1, 2, 3, 4, 9 or 10.

Example 2.2.1

Answer:

345,726 is divisible by 1 because all whole numbers are divisible by 1.

345,726 is divisible by 2 because 345,726 is an even number.

345,726 is divisible by 3 because the sum of the digits 3+4+5+7+2+6 = 27 and 27

is divisible by 3.

345,726 is not divisible by 5 because the rightmost digit is not 5 or 0.

345,726 is divisible by 6 because 345,726 is divisible by 2 and by 3.

Example 2.2.2

Answer:

68,970 is divisible by 1 because all whole numbers are divisible by 1.

68,970 is divisible by 2 because 68,970 is an even number.

68,970 is divisible by 3 because the sum of the digits 6+8+9+7= 30 and 30 is

divisible by 3.

68,970 is not divisible by 4 because the number formed by the 2 rightmost

digits is 70, but 70 is not divisible by 4.

68,970 is not divisible by 9 because the sum of the digits 6+8+9+7= 30 and 30 is

not divisible by 9.

68,970 is divisible by 10 because the rightmost digit is a zero.


Determine whether 476,306 is divisible by 9 by applying an appropriate divisibility

rule. Check your answer by performing the long division.

Answer: Since the sum of the digits is 4+7+6+3+0+6 = 26 and 26 is not divisible by

9, this means that 476,306 is not divisible by 9 either. To check the answer, we

perform the long division and note that the remainder is not zero, as expected.

Determine whether 128,975 is divisible by 5 by applying an appropriate divisibility

rule. Check your answer by performing the long division.

Answer: Since the number 128,975 has a digit 5 in the ones place, the number

128,975 is divisible by 5. To check the answer, we perform the long division and

note that the remainder is zero, as expected.

5 2 9 2 2

9 4 7 6 3 0 6

- 4 5

2 6

- 1 8

8 3

- 8 1

2 0

- 1 8

2 6

1 8

8

F

F M

- :

0

Example 2.2.3

Example 2.2.4

Since the reminder is not zero, 9 is not

a factor of 476,306. We also conclude

that 476,306 is not a multiple of 9.


Instructional videos on the application of the Rules of Divisibility can be found in

the following websites:

http://www.youtube.com/watch?v=AXlz_dHmye4

http://www.youtube.com/watch?v=kBhbv4AVDlI

The following questions ask you to determine whether a number is a factor of the

given number. You may use any method to determine this, including the rules of

divisibility that were presented in this section.

1. Is 2 a factor of 7,986?





2 5 7 9 5

5 1 2 8 9 7 5

- 1 0

2 8

- 2 5

3 9

- 3 5

4 7

- 4 5

2 5

2 5

0

F

F M

- :

0

Classwork 2.2

A zero remainder means that the

number 128,975 is divisible by 5.

Hence, 5 is a factor of 128,975 and

128,975 is a multiple of 5.





9. Is 7,872 divisible by 3?


11. Is 9 a factor of 3,673,909?

12. Is 4 a factor of 845,912?

13. Is 2 a factor of 67,932,663?

14. Is 3 a factor of 852,504?

15. Is 9 a factor of 852,504?

16. Is 10 a factor of 89,015?

17. Is 9 a factor of 10,203?
















CW 2.2 Solutions:

1. Yes 2. No 3. Yes 4. Yes 5. No 6. Yes 7. Yes 8. Yes 9. Yes 10. Yes

11. No 12. Yes 13. No 14. Yes 15. No 16. No 17. No 18. Yes

19. Yes 20. Yes 21. Yes 22. No 23. No 24. Yes 25. Yes 26. No

27. Yes 28. Yes 29. Yes 30. No


The following questions ask you to determine whether a number is a factor of the

given number. You may use any method to determine this, including the rules of

divisibility that were presented in this section.



3. Is 2 a factor of 687,421?



6. Is 10 a factor of 16,785?





11. Is 4 a factor of 32,719?

12. Is 2 a factor of 97,456,031?

13. Is 6 a factor of 34,692?






Homework 2.2















HW 2.2 Solutions:

1. Yes 2. No 3. No 4. Yes 5. No 6. No 7. No 8. Yes 9. Yes 10. Yes

11. No 12. No 13. Yes 14. Yes 15. No 16. Yes 17. Yes 18. No

19. Yes 20. Yes 21. No 22. Yes 23. Yes 24. Yes 25. No 26. Yes

27. Yes 28. No 29. Yes 30. Yes


Section 2.3 – Prime Factorization

Recall that a prime number has exactly two different factors: 1 and the

number itself. For your convenience, here again is a list of all the prime numbers

that are less than 1000:

Table of Prime Numbers Less Than 1,000

2 3 5 7 11 13 17 19 23

29 31 37 41 43 47 53 59 61 67

71 73 79 83 89 97 101 103 107 109

113 127 131 137 139 149 151 157 163 167

173 179 181 191 193 197 199 211 223 227

229 233 239 241 251 257 263 269 271 277

281 283 293 307 311 313 317 331 337 347

349 353 359 367 373 379 383 389 397 401

409 419 421 431 433 439 443 449 457 461

463 467 479 487 491 499 503 509 521 523

541 547 557 563 569 571 577 587 593 599

601 607 613 617 619 631 641 643 647 653

659 661 673 677 683 691 701 709 719 727

733 739 743 751 757 761 769 773 787 797

809 811 821 823 827 829 839 853 857 859

863 877 881 883 887 907 911 919 929 937

941 947 953 967 971 977 983 991 997

We have learned that whole numbers have factors, and thus can be written in

factorized form. For example, some factorizations of the number 360 are

360 = 6 × 5 × 12

360 = 1 × 9 × 4 × 10

360 = 18 × 5 × 4

360 = 1 × 360

These are four different factorizations

of 360 because when we multiply the

whole numbers the product is 360.


A factorization of a number shows factors that multiplied together give the

original number. Note that although 4, 6 and 5 are factors of 360, the expression

4 × 6 × 5 is not a factorization of 360 because 4 × 6 × 5 360. Recall that the

symbol means “not equal to.”

Write 5 different factorizations of 2,000.

In some applications, it is useful to factorize a whole number using only prime

factors. The prime factorization of a number entails “breaking” or “splitting” a

number into factors that are prime numbers, and that gives back the original

number when we multiply the prime factors.

For example, the prime factorization of 2,000 is 2 × 2 × 2 × 2 × 5 × 5 × 5

because all these factors of 2,000 are prime numbers, and when we multiply

2 × 2 × 2 × 2 × 5 × 5 × 5 we get back 2,000.

The prime factorization of 90 is 2 × 3 × 3 × 5 because 2 × 3 × 3 × 5 = 90 and

the numbers 2, 3 and 5 are prime.

Note: 1 is not a prime number because it has only one factor: itself 1 × 1 = 1 .

Example 2.3.1

Answer:

2,000 = 1 × 100 × 20

2,000 = 10 × 4 × 50

2,000 = 1 × 2 × 4 × 5 × 10 × 5

2,000 = 1 × 2000

2,000 = 50 × 40


×

×

×

×

A method to find the prime factorization of any whole number involves

constructing a tree of factors. Each factor appearing in the tree must be either a

prime number or a composite number. Hence, 1 should not appear in a tree of

factors because 1 is neither prime nor composite. The approach to construct a

tree of factors is to split, or factor, the original number into a product of prime

and/or composite factors, and then continue splitting these factors until we are

left with prime factors at the end of the branches.

For example, to find the prime factorization of 12, we begin by factoring 12 in any

way we choose, as long as the factors are prime or composite. At the end of the

branches, we will be left with only prime numbers that multiplied together give

the original number we started with (12).

The numbers in red are the prime factors of 12, and so the prime factorization of

12 in expanded form is × × . If you are familiar with exponents, you can

write the prime factorization in exponential form as × . You will learn more

about exponential notation in Section 2.5.

Write the prime factorization of 45 in expanded form.

Using exponents, the prime factorization of 45 in exponential form is given by

45 = 5 × 3 .

Example 2.3.2

Answer: 45 = 5 × 3 × 3


×

× ×

×

×

× ×


Using exponents, the prime factorization of 120 is 120 = 5 × 2 × 3 .


In exponential form, the answer is 350 = 2 × 5 × 7 .

Example 2.3.3

Answer: 120 = 5 × 2 × 2 × 2 × 3

Example 2.3.4

Answer: 350 = 2 × 5 × 5 × 7



In exponential form, the answer is 504 = 2 × 3 × 7

Instructional video on finding the prime factorization of a whole number:

http://www.youtube.com/watch?v=YKXE2rMKPYA

The following website has an interactive tool to help you construct a tree of

factors to find the prime factorization of any whole number:

http://www.softschools.com/math/factors/factor_tree/

Write the prime factorization of each number.

1. 70

2. 100

3. 231

Example 2.3.5

Answer: 504 = 2 × 2 × 2 × 3 × 3 × 7

×

×

×

×

×

Classwork 2.3


4. 441

5. 420

6. 800

7. 3,600

8. 26

9. 98

10. 1,000

11. 111

12. 666

13. 385

14. 900

15. 64

16. 125

17. 4,000

18. 9

19. 52

20. 350

21. 1,600

22. 36

23. 280

24. 243

25. 625


26. 726

27. 2,940

28. 570

29. 3,465

30. 936


CW 2.3 Solutions:

1. 70 = 2 × 5 × 7

2. 100 = 2 × 2 × 5 × 5

3. 231 = 3 × 7 × 11

4. 441 = 3 × 3 × 7 × 7

5. 420 = 2 × 2 × 3 × 5 × 7

6. 800 = 2 × 2 × 2 × 2 × 2 × 5 × 5

7. 3,600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

8. 26 = 2 × 13

9. 98 = 2 × 7 × 7

10. 1,000 = 2 × 2 × 2 × 5 × 5 × 5

11. 111 = 3 × 37

12. 666 = 2 × 3 × 3 × 37

13. 385 = 5 × 7 × 11

14. 900 = 2 × 2 × 3 × 3 × 5 × 5

15. 64 = 2 × 2 × 2 × 2 × 2 × 2

16. 125 = 5 × 5 × 5

17. 4,000 = 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5

18. 9 = 3 × 3

19. 52 = 2 × 2 × 13

20. 350 = 2 × 5 × 5 × 7

21. 1,600 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5

22. 36 = 2 × 2 × 3 × 3

23. 280 = 2 × 2 × 2 × 5 × 7

24. 243 = 3 × 3 × 3 × 3 × 3

25. 625 = 5 × 5 × 5 × 5

26. 726 = 2 × 3 × 11 × 11

27. 2,940 = 2 × 2 × 3 × 5 × 7 × 7

28. 570 = 2 × 3 × 5 × 19

29. 3,465 = 3 × 3 × 5 × 7 × 11

30. 936 = 2 × 2 × 2 × 3 × 3 × 13


Write the prime factorization of each number.

1. 735

2. 180

3. 924

4. 60

5. 2,300

6. 64

7. 80

8. 4,620

9. 81

10. 690

11. 6

12. 700

13. 57

14. 582

15. 105

16. 40

17. 225

18. 9,600

19. 144

20. 72

Homework 2.3


21. 8

22. 7

23. 2,187

24. 1,750

25. 372

26. 4,455

27. 205

28. 9,936

29. 1,100

30. 85


HW 2.3 Solutions:

1. 735 = 3 × 5 × 7 × 7

2. 180 = 2 × 2 × 3 × 3 × 5

3. 924 = 2 × 2 × 3 × 7 × 11

4. 60 = 2 × 2 × 3 × 5

5. 2,300 = 2 × 2 × 5 × 5 × 23

6. 64 = 2 × 2 × 2 × 2 × 2 × 2

7. 80 = 2 × 2 × 2 × 2 × 5

8. 4,620 = 2 × 2 × 3 × 5 × 7 × 11

9. 81 = 3 × 3 × 3 × 3

10. 690 = 2 × 3 × 5 × 23

11. 6 = 2 × 3

12. 700 = 2 × 2 × 5 × 5 × 7

13. 57 = 3 × 19

14. 582 = 2 × 3 × 97

15. 105 = 3 × 5 × 7

16. 40 = 2 × 2 × 2 × 5

17. 225 = 3 × 3 × 5 × 5

18. 9,600 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5

19. 144 = 2 × 2 × 2 × 2 × 3 × 3

20. 72 = 2 × 2 × 2 × 3 × 3

21. 8 = 2 × 2 × 2

22. 7 = 7 a prime number is its own prime factorization

23. 2,187 = 3 × 3 × 3 × 3 × 3 × 3 × 3

24. 1,750 = 2 × 5 × 5 × 5 × 7

25. 372 = 2 × 2 × 3 × 31

26. 4,455 = 3 × 3 × 3 × 3 × 5 × 11

27. 205 = 5 × 41

28. 9,936 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 23

29. 1,100 = 2 × 2 × 5 × 5 × 11

30. 85 = 5 × 17

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Section 2.1 – Factors and Multiples · only whole number that is neither prime nor composite. Table of Prime Numbers Less Than 1,000 ... 8 - : - : prime factorization × . × 1