Factors of 1 to 100 Using Prime Factorization
What are Factors?
Deriving the factors of a number suggests that these factors are natural numbers. This set of natural numbers divides a number evenly without leaving any remainder. In other words, when two numbers are multiplied to result in a product, the numbers that are being multiplied are the factors of the product.
Properties of Factors
- A factor of a number will always be less than, or, equal to that number.
- Other than 0, every number has a minimum of two factors that are 1 and the number itself.
- Factors of any number can be found by multiplication and division operations.
- Divisibility rules can also be applied to determine whether a number is a factor of another number or not.
- A number is evenly divisible by all its factors.
- If the factor of a number is a prime number, then, the factor is known as the prime factor of the number.
- The process of expressing a number as the product of prime numbers, is known as the prime factorization of the number.
- If a number has exactly two factors, then, the number is known as a prime number.
- A number having more than two factors is known as a composite number.
Factors of 1 to 100
The table here shows the factors of 1 to 100 along with their prime factors. This table will also help you in recognizing which of the following natural numbers are prime numbers, and, the numbers that are composite numbers.
Numbers | Factors | Prime Factors | Prime/Composite |
|---|---|---|---|
1 | 1 | - | Neither Prime nor composite |
2 | 1, 2 | 2 | Prime |
3 | 1, 3 | 3 | Prime |
4 | 1, 2, 4 | 2 x 2 | Composite |
5 | 1, 5 | 5 | Prime |
6 | 1, 2, 3, 6 | 2 x 3 | Composite |
7 | 1, 7 | 7 | Prime |
8 | 1, 2, 4, 8 | 2 x 2 x 2 | Composite |
9 | 1, 3, 9 | 3 x 3 | Composite |
10 | 1, 2, 5, 10 | 2 x 5 | Composite |
11 | 1, 11 | 11 | Prime |
12 | 1, 2, 3, 4, 6, 12 | 2 x 2 x 3 | Composite |
13 | 1, 13 | 13 | Prime |
14 | 1, 2, 7, 14 | 2 x 7 | Composite |
15 | 1, 3, 5, 15 | 3 x 5 | Composite |
16 | 1, 2, 4, 8, 16 | 2 x 2 x 2 x 2 | Composite |
17 | 1, 17 | 17 | Prime |
18 | 1, 2, 3, 6, 9, 18 | 2 x 3 x 3 | Composite |
19 | 1, 19 | 19 | Prime |
20 | 1, 2, 4, 5, 10, 20 | 2 x 2 x 5 | Composite |
21 | 1, 3, 7, 21 | 3 x 7 | Composite |
22 | 1, 2, 11, 22 | 2 x 11 | Composite |
23 | 1, 23 | 23 | Prime |
24 | 1, 2, 3, 4, 6, 8, 12, 24 | 2 x 2 x 2 x 3 | Composite |
25 | 1, 5, 25 | 5 x 5 | Composite |
26 | 1, 2, 13, 26 | 2 x 13 | Composite |
27 | 1, 3, 9, 27 | 3 x 3 x 3 | Composite |
28 | 1, 2, 4, 7, 14, 28 | 2 x 2 x 7 | Composite |
29 | 1, 29 | 29 | Prime |
30 | 1, 2, 3, 5, 6, 10, 15, 30 | 2 x 3 x 5 | Composite |
31 | 1, 31 | 31 | Prime |
32 | 1, 2, 4, 8, 16, 32 | 2 x 2 x 2 x 2 x 2 | Composite |
33 | 1, 3, 11, 33 | 3 x 11 | Composite |
34 | 1, 2, 17, 34 | 2 x 17 | Composite |
35 | 1, 5, 7, 35 | 5 x 7 | Composite |
36 | 1, 2, 3, 4, 6, 9, 12, 18, 36 | 2 x 2 x 3 x 3 | Composite |
37 | 1, 37 | 37 | Prime |
38 | 1, 2, 19, 38 | 2 x 19 | Composite |
39 | 1, 3, 13, 39 | 3 x 13 | Composite |
40 | 1, 2, 4, 5, 8, 10, 20, 40 | 2 x 2 x 2 x 5 | Composite |
41 | 1, 41 | 41 | Prime |
42 | 1, 2, 3, 6, 7, 14, 21, 42 | 2 x 3 x 7 | Composite |
43 | 1, 43 | 43 | Prime |
44 | 1, 2, 4, 11, 22, 44 | 2 x 2 x 11 | Composite |
45 | 1, 3, 5, 9, 15, 45 | 3 x 3 x 5 | Composite |
46 | 1, 2, 23, 46 | 2 x 23 | Composite |
47 | 1, 47 | 47 | Prime |
48 | 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 | 2 x 2 x 2 x 2 x 3 | Composite |
49 | 1, 7, 49 | 7 x 7 | Composite |
50 | 1, 2, 5, 10, 25, 50 | 2 x 5 x 5 | Composite |
51 | 1, 3, 17, 51 | 3 x 17 | Composite |
52 | 1, 2, 4, 13, 26, 52 | 2 x 2 x 13 | Composite |
53 | 1, 53 | 53 | Prime |
54 | 1, 2, 3, 6, 9, 18, 27, 54 | 2 x 3 x 3 x 3 | Composite |
55 | 1, 5, 11, 55 | 5 x 11 | Composite |
56 | 1, 2, 4, 7, 8, 14, 28, 56 | 2 x 2 x 2 x 7 | Composite |
57 | 1, 3, 19, 57 | 3 x 19 | Composite |
58 | 1, 2, 29, 58 | 2 x 29 | Composite |
59 | 1, 59 | 59 | Prime |
60 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 | 2 x 2 x 3 x 5 | Composite |
61 | 1, 61 | 61 | Prime |
62 | 1, 2, 31, 62 | 2 x 31 | Composite |
63 | 1, 3, 7, 9, 21, 63 | 3 x 3 x 7 | Composite |
64 | 1, 2, 4, 8, 16, 32, 64 | 2 x 2 x 2 x 2 x 2 x 2 | Composite |
65 | 1, 5, 13, 65 | 5 x 13 | Composite |
66 | 1, 2, 3, 6, 11, 22, 33, 66 | 2 x 3 x 11 | Composite |
67 | 1, 67 | 67 | Prime |
68 | 1, 2, 4, 17, 34, 68 | 2 x 2 x 17 | Composite |
69 | 1, 3, 23, 69 | 3 x 23 | Composite |
70 | 1, 2, 5, 7, 10, 14, 35, 70 | 2 x 5 x 7 | Composite |
71 | 1, 71 | 71 | Prime |
72 | 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 | 2 x 2 x 2 x 3 x 3 | Composite |
73 | 1, 73 | 73 | Prime |
74 | 1, 2, 37, 74 | 2 x 37 | Composite |
75 | 1, 3, 5, 15, 25, 75 | 3 x 5 x 5 | Composite |
76 | 1, 2, 4, 19, 38, 76 | 2 x 2 x 19 | Composite |
77 | 1, 7, 11, 77 | 7 x 11 | Composite |
78 | 1, 2, 3, 6, 13, 26, 39, 78 | 2 x 3 x 13 | Composite |
79 | 1, 79 | 79 | Prime |
80 | 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 | 2 x 2 x 2 x 2 x 5 | Composite |
81 | 1, 3, 9, 27, 81 | 3 x 3 x 3 x 3 | Composite |
82 | 1, 2, 41, 82 | 2 x 41 | Composite |
83 | 1, 83 | 83 | Prime |
84 | 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 | 2 x 2 x 3 x 7 | Composite |
85 | 1, 5, 17, 85 | 5 x 17 | Composite |
86 | 1, 2, 43, 86 | 2 x 43 | Composite |
87 | 1, 3, 29, 87 | 3 x 29 | Composite |
88 | 1, 2, 4, 8, 11, 22, 44, 88 | 2 x 2 x 2 x 11 | Composite |
89 | 1, 89 | 89 | Prime |
90 | 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 | 2 x 3 x 3 x 5 | Composite |
91 | 1, 7, 13, 91 | 7 x 13 | Composite |
92 | 1, 2, 4, 23, 46, 92 | 2 x 2 x 23 | Composite |
93 | 1, 3, 31, 93 | 3 x 31 | Composite |
94 | 1, 2, 47, 94 | 2 x 47 | Composite |
95 | 1, 5, 19, 95 | 5 x 19 | Composite |
96 | 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 | 2 x 2 x 2 x 2 x 2 x 3 | Composite |
97 | 1, 97 | 97 | Prime |
98 | 1, 2, 7, 14, 49, 98 | 2 x 7 x 7 | Composite |
99 | 1, 3, 9, 11, 33, 99 | 3 x 3 x 11 | Composite |
100 | 1, 2, 4, 5, 10, 20, 25, 50, 100 | 2 x 2 x 5 x 5 | Composite |
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Solved Examples
Example 1: State whether this statement is true or false: Do all even numbers have 2 as a factor?
Solution:
True, since all even numbers have 2 as one of their factors.
Example 2: Find all the factors of 23.
Solution: 23 is a prime number. The only two numbers that divide 23 completely are 1 and 23 itself. Thus, the factors of 23 are 1 and 23.
Example 3: Find all the factors of 27.
Solution:
The factors of 27 are 1, 3, 9, and 27.
Example 4: Find the common factors of 55 and 100.
Solution:
To find the common factors of 55 and 100, list the factors of 55 and 100.
Factors of 55 : 1, 5, 11, 55
Factors of 100 : 1, 2, 4, 5, 10, 20, 25, 50, 100
Therefore, the common factors of 55 and 100: 1 and 5.
A factor of any number is a number that evenly divides the original number. For example, 1 can divide every number, thus 1 is a factor of every number.
The prime factors of any number are the factors of that number, and which are also the prime numbers as well.
No, factors cannot be fractions or decimals.
The prime factorization of a number refers to expressing the number as the product of two or more prime numbers. For example, the prime factorization of 30 = 2 x 3 x 5.