martes, 10 de octubre de 2017

¿Cúantas veces aparece el 2 como factor en el número 100! ?

Resolución:

2(lo añadimos al final)
4 = 2 * 2                      2
6 = 2 * 3                      3
8 = 2 * 2 * 2                  6
9 = 3 * 3
10 = 2 * 5                     7
12 = 2 * 2 * 3                 9
14 = 2 * 7                     10
15 = 3 * 5
16 = 2 * 2 * 2 * 2             14
18 = 2 * 3 * 3                 15
20 = 2 * 2 * 5                 17
21 = 3 * 7
22 = 2 * 11                    18
24 = 2 * 2 * 2 * 3             21
25 = 5 * 5
26 = 2 * 13                    22
27 = 3 * 3 * 3
28 = 2 * 2 * 7                 24
30 = 2 * 3 * 5                 25
32 = 2 * 2 * 2 * 2 * 2 30
33 = 3 * 11
34 = 2 * 17                    31
35 = 5 * 7
36 = 2 * 2 * 3 * 3             33
38 = 2 * 19                    34
39 = 3 * 13
40 = 2 * 2 * 2 * 5             37
42 = 2 * 3 * 7                 38
44 = 2 * 2 * 11        40
45 = 3 * 3 * 5
46 = 2 * 23                    41
48 = 2 * 2 * 2 * 2 * 3 45
49 = 7 * 7
50 = 2 * 5 * 5                 46
51 = 3 * 17
52 = 2 * 2 * 13        48
54 = 2 * 3 * 3 * 3             49
55 = 5 * 11
56 = 2 * 2 * 2 * 7             52
57 = 3 * 19
58 = 2 * 29                    53
60 = 2 * 2 * 3 * 5             55
62 = 2 * 31                    56
63 = 3 * 3 * 7
64 = 2 * 2 * 2 * 2 * 2 * 2     62
65 = 5 * 13
66 = 2 * 3 * 11        63
68 = 2 * 2 * 17        65
69 = 3 * 23
70 = 2 * 5 * 7                 66
72 = 2 * 2 * 2 * 3 * 3 69
74 = 2 * 37                    70
75 = 3 * 5 * 5
76 = 2 * 2 * 19        7281 = 3 * 3 * 3 * 3
82 = 2 * 41                    78
84 = 2 * 2 * 3 * 7             80
85 = 5 * 17
86 = 2 * 43                    81
87 = 3 * 29
88 = 2 * 2 * 2 * 11            84
90 = 2 * 3 * 3 * 5             85
91 = 7 * 13
92 = 2 * 2 * 23        87
93 = 3 * 31
94 = 2 * 47                    88
95 = 5 * 19
96 = 2 * 2 * 2 * 2 * 2 * 3     93
98 = 2 * 7 * 7                 94
99 = 3 * 3 * 11
100 = 2 * 2 * 5 * 5            96 + 1 = 97
77 = 7 * 11
78 = 2 * 3 * 13        73
80 = 2 * 2 * 2 * 2 * 5 77

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