Basic factoring will be automatically and instantaneously completed through this applet:
http://conceptualeclipse.googlepages.com/primefactorization
(no download necessary, works on all platforms)
The applet will clearly tell you the prime factors, number of prime factors, and number of unique prime factors of any integer between -1,000,000,000 and 1,000,000,000 immediately.
For convenience's sake, here is a list of the factors of all numbers between 1 and 100
They are presented in the following format
Number X
---First factor of number X
---Second factor of number X
---Third factor of number X
1
---1
2
---1
---2
3
---1
---3
4
---1
---2
---4
5
---1
---5
6
---1
---2
---3
---6
7
---1
---7
8
---1
---2
---4
---8
9
---1
---3
---9
10
---1
---2
---5
---10
11
---1
---11
12
---1
---2
---3
---4
---6
---12
13
---1
---13
14
---1
---2
---7
---14
15
---1
---3
---5
---15
16
---1
---2
---4
---8
---16
17
---1
---17
18
---1
---2
---3
---6
---9
---18
19
---1
---19
20
---1
---2
---4
---5
---10
---20
21
---1
---3
---7
---21
22
---1
---2
---11
---22
23
---1
---23
24
---1
---2
---3
---4
---6
---8
---12
---24
25
---1
---5
---25
26
---1
---2
---13
---26
27
---1
---3
---9
---27
28
---1
---2
---4
---7
---14
---28
29
---1
---29
30
---1
---2
---3
---5
---6
---10
---15
---30
31
---1
---31
32
---1
---2
---4
---8
---16
---32
33
---1
---3
---11
---33
34
---1
---2
---17
---34
35
---1
---5
---7
---35
36
---1
---2
---3
---4
---6
---9
---12
---18
---36
37
---1
---37
38
---1
---2
---19
---38
39
---1
---3
---13
---39
40
---1
---2
---4
---5
---8
---10
---20
---40
41
---1
---41
42
---1
---2
---3
---6
---7
---14
---21
---42
43
---1
---43
44
---1
---2
---4
---11
---22
---44
45
---1
---3
---5
---9
---15
---45
46
---1
---2
---23
---46
47
---1
---47
48
---1
---2
---3
---4
---6
---8
---12
---16
---24
---48
49
---1
---7
---49
50
---1
---2
---5
---10
---25
---50
51
---1
---3
---17
---51
52
---1
---2
---4
---13
---26
---52
53
---1
---53
54
---1
---2
---3
---6
---9
---18
---27
---54
55
---1
---5
---11
---55
56
---1
---2
---4
---7
---8
---14
---28
---56
57
---1
---3
---19
---57
58
---1
---2
---29
---58
59
---1
---59
60
---1
---2
---3
---4
---5
---6
---10
---12
---15
---20
---30
---60
61
---1
---61
62
---1
---2
---31
---62
63
---1
---3
---7
---9
---21
---63
64
---1
---2
---4
---8
---16
---32
---64
65
---1
---5
---13
---65
66
---1
---2
---3
---6
---11
---22
---33
---66
67
---1
---67
68
---1
---2
---4
---17
---34
---68
69
---1
---3
---23
---69
70
---1
---2
---5
---7
---10
---14
---35
---70
71
---1
---71
72
---1
---2
---3
---4
---6
---8
---9
---12
---18
---24
---36
---72
73
---1
---73
74
---1
---2
---37
---74
75
---1
---3
---5
---15
---25
---75
76
---1
---2
---4
---19
---38
---76
77
---1
---7
---11
---77
78
---1
---2
---3
---6
---13
---26
---39
---78
79
---1
---79
80
---1
---2
---4
---5
---8
---10
---16
---20
---40
---80
81
---1
---3
---9
---27
---81
82
---1
---2
---41
---82
83
---1
---83
84
---1
---2
---3
---4
---6
---7
---12
---14
---21
---28
---42
---84
85
---1
---5
---17
---85
86
---1
---2
---43
---86
87
---1
---3
---29
---87
88
---1
---2
---4
---8
---11
---22
---44
---88
89
---1
---89
90
---1
---2
---3
---5
---6
---9
---10
---15
---18
---30
---45
---90
91
---1
---7
---13
---91
92
---1
---2
---4
---23
---46
---92
93
---1
---3
---31
---93
94
---1
---2
---47
---94
95
---1
---5
---19
---95
96
---1
---2
---3
---4
---6
---8
---12
---16
---24
---32
---48
---96
97
---1
---97
98
---1
---2
---7
---14
---49
---98
99
---1
---3
---9
---11
---33
---99
100
---1
---2
---4
---5
---10
---20
---25
---50
---100
There is no simple relationshipp between a number and the count of its factors.
There isn't any, and it is quite simple to prove that. Suppose there is a number with the most factors and suppose that number is X. Now consider Y = 2*X. Y has all the factors of X and it has another factor, which is 2. So Y has more factors than X. This contradicts the statement that X has the most factors. Therefore, there is no number with the most factors.
There isn't any, and it is quite simple to prove that. Suppose there is a number with the most factors and suppose that number is X. Now consider Y = 2*X. Y has all the factors of X and it has another factor, which is 2. So Y has more factors than X. This contradicts the statement that X has the most factors. Therefore, there is no number with the most factors.
The number 76 as a product of its prime factors is: 2 x 2 x 19
The prime factors are: 2 x 2 x 23
If you know the prime factorization of a number, you can find out the total number of factors. Example: 210 2^1 x 3^1 x 5^1 x 7^1 = 210 Add one to the exponents and multiply them. 2 x 2 x 2 x 2 = 16, the total number of factors. Example: 72 2^3 x 3^2 = 72 4 x 3 = 12 72 has 12 factors
Factors of a numbers are numbers multiplied to get that number e.g. factors of 8 = 1,2,4,8 (1 x 8) (4x2) factors of 12= 1,2,3,4,6,12 (1 x 12) (2 x 6) (3 x 4) hope this helped :*
The exponent
exponent
the exponent
Identify the prime factors of 625 which are : 5 x 5 x 5 x 5 = 625. The factors of 625 are therefore 1 x 625, 5 x 125 and 25 x 25. As the number 25 is effectively duplicated then 625 has 5 factors (1, 5, 25, 125 & 625)
The number 60 as a product of prime factors is: 2 x 3 x 5 = 30