A B C
Homework

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

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.

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