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Learning Math Home
Number and Operations Session 5: Solutions
 
Session 5 Part A Part B Part C Homework
 
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A B C
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Solutions for Session5, Part C

See solutions for Problems: C1 | C2


Problem C1

a. 

Prime Numbers: Two Factors

Three Factors

Four Factors

Five Factors

Six or More Factors

 2: 1, 2

 4: 1, 2, 4

 6: 1, 2, 3, 6

 16: 1, 2, 4, 8, 16

12:

1, 2, 3, 4, 6, 12

 3: 1, 3

 9: 1, 3, 9

 8: 1, 2, 4, 8

 

18:

1, 2, 3, 6, 9, 18

 5: 1, 5

 25: 1, 5, 25

 10: 1, 2, 5, 10

 

20:

1, 2, 4, 5, 10, 20

 7: 1, 7

 

 14: 1, 2, 7, 14

 

24:

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

 11: 1, 11

 

 15: 1, 3, 5, 15

 

28:

1, 2, 4, 7, 14, 28

 13: 1, 13

 

 21: 1, 3, 7, 21

 

30:

1, 2, 3, 5, 6, 10, 15, 30

 17: 1, 17

 

 22: 1, 2, 11, 22

 

32:

1, 2, 4, 8, 16, 32

 19: 1, 19

 

 26: 1, 2, 13, 26

 

36:

1, 2, 3, 4, 6, 9, 12, 18, 36

 23: 1, 23

 

 27: 1, 3, 9, 27

 

 

 29: 1, 29

 

 33: 1, 3, 11, 33

 

 

 31: 1, 31

 

 34: 1, 2, 17, 34

 

 

 

 

 35: 1, 5, 7, 35

 

 


b. 

Prime Numbers

Two Prime Factors

Three Prime Factors

Four Prime Factors

Five Prime Factors

 2

 4: 22

 8: 23

 16: 24

 32: 25

 3

 6: 3 • 2

 12: 3 • 22

 24: 3 • 23

 

 5

 9: 32

 18: 32 • 2

 36: 32 • 22

 

 7

 10: 5 • 2

 20: 5 • 22

 

 

 11

 14: 7 • 2

 27: 33

 

 

 13

 15: 5 • 3

 28: 7 • 22

 

 

 17

 21: 7 • 3

 30: 5 • 3 • 2

 

 

 19

 22: 11 • 2

 

 

 

 23

 25: 52

 

 

 

 29

 26: 13 • 2

 

 

 

 3

 33: 11 • 3

 

 

 

 

 34: 17 • 2

 

 

 

 

 35: 7 • 5

 

 

 

<< back to Problem C1


 

Problem C2

Looking at the prime factorization of numbers, you can tell how many factors a number will have in total. For example, the prime factorization of 2 is 21, and 2 has two factors in total, 1 and 2. The prime factorization of 4 is 22, and it has three factors in all: 1, 2, and 4. To further investigate this pattern, let's look at the following:

36 = 32 • 22 will have (2 + 1) • (2 + 1), or nine factors total.

24 = 23 • 31 will have (3 + 1) • (1 + 1), or eight factors total.

81 = 34 will have (4 + 1), or five factors total.

<< back to Problem C2


 

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