Factors of 1 to 100: Full Table with Prime Factors

How to read the table

Find the number in the first column. The second column lists every whole number that divides it exactly. The third says how many there are, and the fourth writes the number as a product of primes. Numbers in the first column that are links have a page of their own with full working. For any other number, or a larger one, use the factor finder.

What to notice

Primes have exactly two factors. There are 25 primes up to 100, and their rows are shaded.
1 has a single factor, itself, so it is neither prime nor composite.
Perfect squares have an odd count of factors. They are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. Every other number has an even count, because factors come in pairs.
The most factors. No number up to 100 has more than 12 factors. Those with 12 are 60, 72, 84, 90 and 96.
Squares of primes have exactly three factors: 4, 9, 25 and 49.

Number	Factors	How many	Prime factorisation
1	1	1	none
2	1, 2	2	2
3	1, 3	2	3
4	1, 2, 4	3	2²
5	1, 5	2	5
6	1, 2, 3, 6	4	2 × 3
7	1, 7	2	7
8	1, 2, 4, 8	4	2³
9	1, 3, 9	3	3²
10	1, 2, 5, 10	4	2 × 5
11	1, 11	2	11
12	1, 2, 3, 4, 6, 12	6	2² × 3
13	1, 13	2	13
14	1, 2, 7, 14	4	2 × 7
15	1, 3, 5, 15	4	3 × 5
16	1, 2, 4, 8, 16	5	2⁴
17	1, 17	2	17
18	1, 2, 3, 6, 9, 18	6	2 × 3²
19	1, 19	2	19
20	1, 2, 4, 5, 10, 20	6	2² × 5
21	1, 3, 7, 21	4	3 × 7
22	1, 2, 11, 22	4	2 × 11
23	1, 23	2	23
24	1, 2, 3, 4, 6, 8, 12, 24	8	2³ × 3
25	1, 5, 25	3	5²
26	1, 2, 13, 26	4	2 × 13
27	1, 3, 9, 27	4	3³
28	1, 2, 4, 7, 14, 28	6	2² × 7
29	1, 29	2	29
30	1, 2, 3, 5, 6, 10, 15, 30	8	2 × 3 × 5
31	1, 31	2	31
32	1, 2, 4, 8, 16, 32	6	2⁵
33	1, 3, 11, 33	4	3 × 11
34	1, 2, 17, 34	4	2 × 17
35	1, 5, 7, 35	4	5 × 7
36	1, 2, 3, 4, 6, 9, 12, 18, 36	9	2² × 3²
37	1, 37	2	37
38	1, 2, 19, 38	4	2 × 19
39	1, 3, 13, 39	4	3 × 13
40	1, 2, 4, 5, 8, 10, 20, 40	8	2³ × 5
41	1, 41	2	41
42	1, 2, 3, 6, 7, 14, 21, 42	8	2 × 3 × 7
43	1, 43	2	43
44	1, 2, 4, 11, 22, 44	6	2² × 11
45	1, 3, 5, 9, 15, 45	6	3² × 5
46	1, 2, 23, 46	4	2 × 23
47	1, 47	2	47
48	1, 2, 3, 4, 6, 8, 12, 16, 24, 48	10	2⁴ × 3
49	1, 7, 49	3	7²
50	1, 2, 5, 10, 25, 50	6	2 × 5²
51	1, 3, 17, 51	4	3 × 17
52	1, 2, 4, 13, 26, 52	6	2² × 13
53	1, 53	2	53
54	1, 2, 3, 6, 9, 18, 27, 54	8	2 × 3³
55	1, 5, 11, 55	4	5 × 11
56	1, 2, 4, 7, 8, 14, 28, 56	8	2³ × 7
57	1, 3, 19, 57	4	3 × 19
58	1, 2, 29, 58	4	2 × 29
59	1, 59	2	59
60	1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60	12	2² × 3 × 5
61	1, 61	2	61
62	1, 2, 31, 62	4	2 × 31
63	1, 3, 7, 9, 21, 63	6	3² × 7
64	1, 2, 4, 8, 16, 32, 64	7	2⁶
65	1, 5, 13, 65	4	5 × 13
66	1, 2, 3, 6, 11, 22, 33, 66	8	2 × 3 × 11
67	1, 67	2	67
68	1, 2, 4, 17, 34, 68	6	2² × 17
69	1, 3, 23, 69	4	3 × 23
70	1, 2, 5, 7, 10, 14, 35, 70	8	2 × 5 × 7
71	1, 71	2	71
72	1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72	12	2³ × 3²
73	1, 73	2	73
74	1, 2, 37, 74	4	2 × 37
75	1, 3, 5, 15, 25, 75	6	3 × 5²
76	1, 2, 4, 19, 38, 76	6	2² × 19
77	1, 7, 11, 77	4	7 × 11
78	1, 2, 3, 6, 13, 26, 39, 78	8	2 × 3 × 13
79	1, 79	2	79
80	1, 2, 4, 5, 8, 10, 16, 20, 40, 80	10	2⁴ × 5
81	1, 3, 9, 27, 81	5	3⁴
82	1, 2, 41, 82	4	2 × 41
83	1, 83	2	83
84	1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84	12	2² × 3 × 7
85	1, 5, 17, 85	4	5 × 17
86	1, 2, 43, 86	4	2 × 43
87	1, 3, 29, 87	4	3 × 29
88	1, 2, 4, 8, 11, 22, 44, 88	8	2³ × 11
89	1, 89	2	89
90	1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90	12	2 × 3² × 5
91	1, 7, 13, 91	4	7 × 13
92	1, 2, 4, 23, 46, 92	6	2² × 23
93	1, 3, 31, 93	4	3 × 31
94	1, 2, 47, 94	4	2 × 47
95	1, 5, 19, 95	4	5 × 19
96	1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96	12	2⁵ × 3
97	1, 97	2	97
98	1, 2, 7, 14, 49, 98	6	2 × 7²
99	1, 3, 9, 11, 33, 99	6	3² × 11
100	1, 2, 4, 5, 10, 20, 25, 50, 100	9	2² × 5²

Number

Factors

How many

Prime factorisation

none

1, 2

1, 3

1, 2, 4

2²

1, 5

1, 2, 3, 6

2 × 3

1, 7

1, 2, 4, 8

2³

1, 3, 9

3²

1, 2, 5, 10

2 × 5

1, 11

1, 2, 3, 4, 6, 12

2² × 3

1, 13

1, 2, 7, 14

2 × 7

1, 3, 5, 15

3 × 5

1, 2, 4, 8, 16

2⁴

1, 17

1, 2, 3, 6, 9, 18

2 × 3²

1, 19

1, 2, 4, 5, 10, 20

2² × 5

1, 3, 7, 21

3 × 7

1, 2, 11, 22

2 × 11

1, 23

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

2³ × 3

1, 5, 25

5²

1, 2, 13, 26

2 × 13

1, 3, 9, 27

3³

1, 2, 4, 7, 14, 28

2² × 7

1, 29

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

2 × 3 × 5

1, 31

1, 2, 4, 8, 16, 32

2⁵

1, 3, 11, 33

3 × 11

1, 2, 17, 34

2 × 17

1, 5, 7, 35

5 × 7

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

2² × 3²

1, 37

1, 2, 19, 38

2 × 19

1, 3, 13, 39

3 × 13

1, 2, 4, 5, 8, 10, 20, 40

2³ × 5

1, 41

1, 2, 3, 6, 7, 14, 21, 42

2 × 3 × 7

1, 43

1, 2, 4, 11, 22, 44

2² × 11

1, 3, 5, 9, 15, 45

3² × 5

1, 2, 23, 46

2 × 23

1, 47

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

2⁴ × 3

1, 7, 49

7²

1, 2, 5, 10, 25, 50

2 × 5²

1, 3, 17, 51

3 × 17

1, 2, 4, 13, 26, 52

2² × 13

1, 53

1, 2, 3, 6, 9, 18, 27, 54

2 × 3³

1, 5, 11, 55

5 × 11

1, 2, 4, 7, 8, 14, 28, 56

2³ × 7

1, 3, 19, 57

3 × 19

1, 2, 29, 58

2 × 29

1, 59

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

2² × 3 × 5

1, 61

1, 2, 31, 62

2 × 31

1, 3, 7, 9, 21, 63

3² × 7

1, 2, 4, 8, 16, 32, 64

2⁶

1, 5, 13, 65

5 × 13

1, 2, 3, 6, 11, 22, 33, 66

2 × 3 × 11

1, 67

1, 2, 4, 17, 34, 68

2² × 17

1, 3, 23, 69

3 × 23

1, 2, 5, 7, 10, 14, 35, 70

2 × 5 × 7

1, 71

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

2³ × 3²

1, 73

1, 2, 37, 74

2 × 37

1, 3, 5, 15, 25, 75

3 × 5²

1, 2, 4, 19, 38, 76

2² × 19

1, 7, 11, 77

7 × 11

1, 2, 3, 6, 13, 26, 39, 78

2 × 3 × 13

1, 79

1, 2, 4, 5, 8, 10, 16, 20, 40, 80

2⁴ × 5

1, 3, 9, 27, 81

3⁴

1, 2, 41, 82

2 × 41

1, 83

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

2² × 3 × 7

1, 5, 17, 85

5 × 17

1, 2, 43, 86

2 × 43

1, 3, 29, 87

3 × 29

1, 2, 4, 8, 11, 22, 44, 88

2³ × 11

1, 89

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

2 × 3² × 5

1, 7, 13, 91

7 × 13

1, 2, 4, 23, 46, 92

2² × 23

1, 3, 31, 93

3 × 31

1, 2, 47, 94

2 × 47

1, 5, 19, 95

5 × 19

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

2⁵ × 3

1, 97

1, 2, 7, 14, 49, 98

2 × 7²

1, 3, 9, 11, 33, 99

3² × 11

100

1, 2, 4, 5, 10, 20, 25, 50, 100

2² × 5²

Using the table

To find common factors of two numbers, read both rows and pick the numbers that appear in each. For 48 and 60 the common factors are 1, 2, 3, 4, 6 and 12, so the HCF is 12. To simplify a fraction such as 48/60, divide top and bottom by that HCF to get 4/5. To check whether a number is prime, see whether its row has just two entries.

The table is also a good place to practise. Cover the factor column, pick a number and write its factors, then uncover and check. Ten numbers a day covers the table in ten days.

Read more: what factors are, prime factorisation, HCF and LCM.