Prime Factorization Table

In mathematics, prime factorization is one interesting topic in number theory. The process of the positive integers in which they are dividing the integer exactly and also without a remainder value is called as Prime factorization. These types of numbers can be divided by 1 or itself then it is called as prime numbers.

Some of the prime numbers are 2, 3, 5, 7, 9, 11, and 13…

A factor is a number that perfectly divides another number. For example, 2 is a factor of 4 and 3 is a factor of 6. Also, 4 is not a factor of 6 because 6 is not divisible by 4. Every number has a minimum of two factors - 1 and itself. A number which has only two factors (1 and itself) is known as a prime number. A number which has more than 2 factors is known as composite. 5 is an example of a prime number (factors : 1 and 5) and 10 is an example of a composite number (factors: 1, 2, 5 and 10).

Factorization, the method of reducing a number into a product of its prime factors, is a very handy tool. Factorization is essential in finding the greatest common divisor and the least common multiple. These are in turn used to add or subtract fractions. More advanced forms of factorization are made use of in algebraic addition and subtraction.

Prime factorization table - Definitions:

NUMBERS	FACTORS	NUMBER OF FACTORS
1	1	1
2	1, 2	2
3	1, 3	2
4	1, 2, 4	3
5	1, 5	2
6	1, 2, 3, 6	4
7	1, 7	2
8	1, 2, 4, 8	4
9	1, 3, 9	3
10	1, 2, 5, 10	4
11	1, 11	2
12	1, 2, 3, 4, 6, 12	6
13	1, 13	2
14	1, 2, 7, 14	4
15	1, 3, 5, 15	4
16	1, 2, 4, 8, 16	5
17	1, 17	2
18	1, 2, 3, 6, 9, 18	6
19	1, 19	2
20	1, 2, 4, 5, 10, 20	6
21	1, 3, 7, 21	4
22	1, 2, 11, 22	4
23	1, 23	2
24	1, 2, 3, 4, 6, 8, 12, 24	8
25	1, 5, 25	3
26	1, 2, 13, 26	4
27	1, 3, 9, 27	4
28	1, 2, 4, 7, 14, 28	6
29	1, 29	2
30	1, 2, 3, 5, 6, 10, 15, 30	8
31	1, 31	2
32	1, 2, 4, 8, 16, 32	6
33	1, 3, 11, 33	4
34	1, 2, 17, 34	4
35	1, 5, 7, 35	4
36	1, 2, 3, 4, 6, 9, 12, 18, 36	9
37	1, 37	2
38	1, 2, 19, 38	4
39	1, 3, 13, 39	4
40	1, 2, 4, 5, 8, 10, 20, 40	8
41	1, 41	2
42	1, 2, 3, 6, 7, 14, 21, 42	8
43	1, 43	2
44	1, 2, 4, 11, 22, 44	6
45	1, 3, 5, 9, 15, 45	6
46	1, 2, 23, 46	4
47	1, 47	2
48	1, 2, 3, 4, 6, 8, 12, 16, 24, 48	10
49	1, 7, 49	3
50	1, 2, 5, 10, 25, 50	6
51	1, 3, 17, 51	4
52	1, 2, 4, 13, 26, 52	6
53	1, 53	2
54	1, 2, 3, 6, 9, 18, 27, 54	8
55	1, 5, 11, 55	4
56	1, 2, 4, 7, 8, 14, 28, 56	8
57	1, 3, 19, 57	4
58	1, 2, 29, 58	4
59	1, 59	2
60	1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60	12
61	1, 61	2
62	1, 2, 31, 62	4
63	1, 3, 7, 9, 21, 63	6
64	1, 2, 4, 8, 16, 32, 64	7
65	1, 5, 13, 65	4
66	1, 2, 3, 6, 11, 22, 33, 66	8
67	1, 67	2
68	1, 2, 4, 17, 34, 68	6
69	1, 3, 23, 69	4
70	1, 2, 5, 7, 10, 14, 35, 70	8
71	1, 71	2
72	1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36,72	12
73	1, 73	2
74	1, 2, 37, 74	4
75	1, 3, 5, 15, 25, 75	6
76	1, 2, 4, 19, 38, 76	6
77	1, 7, 11, 77	4
78	1, 2, 3, 6, 13, 26, 39, 78	8
79	1, 79	2
80	1, 2, 4, 5, 8, 10, 16, 20, 40, 80	10
81	1, 3, 9, 27, 81	5
82	1, 2, 41, 82	4
83	1, 83	2
84	1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84	12
85	1, 5, 17, 85	4
86	1, 2, 43, 86	4
87	1, 3, 29, 87	4
88	1, 2, 4, 8, 11, 22, 44, 88	8
89	1, 89	2
90	1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90	12
91	1, 7, 13, 91	4
92	1, 2, 4, 23, 46, 92	6
93	1, 3, 31, 93	4
94	1, 2, 47, 94	4
95	1, 5, 19, 95	4
96	1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96	12
97	1, 97	2
98	1, 2, 7, 14, 49,98	6
99	1, 3, 9, 11, 33, 99	6
100	1, 2, 4, 5, 10, 20, 25, 50, 100	9
101	1, 101	2
102	1, 2, 3, 6, 17, 34, 51, 102	8
103	1, 103	2
104	1, 2, 4, 8, 13, 26, 52, 104	8
105	1, 3, 5, 7, 15, 21, 35, 105	8
106	1, 2, 53, 106	4
107	1, 107	2
108	1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108	12
109	1, 109	2
110	1, 2, 5, 10, 11, 22, 55, 110	8
111	1, 3, 37, 111	4
112	1, 2, 4, 7, 8, 14, 16, 28, 56, 112	10
113	1, 113	2
114	1, 2, 3, 6, 19, 38, 57, 114	8
115	1, 5, 23, 115	4
116	1, 2, 4, 29, 58, 116	6
117	1, 3, 9, 13, 39, 117	6
118	1, 2, 59, 118	4
119	1, 7, 17, 119	4
120	1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120	16
121	1, 11, 121	3
122	1, 2, 61, 122	4
123	1, 3, 41, 123	4
124	1, 2, 4, 31, 62, 124	6
125	1, 5, 25, 125	4
126	1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126	12
127	1, 127	2
128	1, 2, 4, 8, 16, 32, 64, 128	8
129	1, 3, 43, 129	4
130	1, 2, 5, 10, 13, 26, 65, 130	8
131	1, 131	2
132	1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132	12
133	1, 7, 19, 133	4
134	1, 2, 67, 134	4
135	1, 3, 5, 9, 15, 27, 45, 135	8
136	1, 2, 4, 8, 17, 34, 68, 136	8
137	1, 137	2
138	1, 2, 3, 6, 23, 46, 69, 138	8
139	1, 139	2
140	1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140	12
141	1, 3, 47, 141	4
142	1, 2, 71, 142	4
143	1,11, 13, 143	4
144	1, 2, 3, 5, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144	15
145	1, 5, 29, 145	4
146	1, 2, 73, 146	4
147	1, 3, 7, 21, 49, 147	6
148	1, 2, 4, 37, 74, 148	6
149	1, 149	2
150	1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150	12
151	1, 151	2
152	1, 2, 4, 8, 19, 38, 76, 152	8
153	1, 3, 9, 17, 51, 153	6
154	1, 2, 7, 11, 14, 22, 77, 154	8
155	1, 5, 31, 155	4
156	1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156	12
157	1, 157	2
158	1, 2, 79, 158	4
159	1, 3, 53, 159	4
160	1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160	12
161	1, 7, 23, 161	4
162	1, 2, 3, 6, 9, 18, 27, 54, 81, 162	10
163	1, 163	2
164	1, 2, 4, 41, 82, 164	6
165	1, 3, 5, 11, 15, 33, 55, 165	8
166	1, 2, 83, 166	4
167	1, 167	2
168	1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168	16
169	1, 13, 169	3
170	1, 2, 5, 10, 17, 34, 85, 170	8
171	1, 3, 9, 19, 57, 171	6
172	1, 2, 4, 43, 86, 172	6
173	1, 173	2
174	1, 2, 3, 6, 29, 58, 87, 174	8
175	1, 5, 7, 25, 35, 175	6
176	1, 2, 4, 8, 11, 16, 22, 44, 88, 176	10
177	1, 3, 59, 177	4
178	1, 2, 89, 178	4
179	1, 179	2
180	1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180	18
181	1, 181	2
182	1, 2, 7, 13, 14, 26, 91, 182	8
183	1, 3, 61, 183	4
184	1, 2, 4, 8, 23, 46, 92, 184	8
185	1, 5, 37, 185	4
186	1, 2, 3, 6, 31, 62, 93, 186	8
187	1, 11, 17, 187	4
188	1, 2, 3, 47, 94, 188	6
189	1, 3, 6, 9, 21, 27, 63, 189	8
190	1, 2, 5, 10, 19, 38, 95, 190	8
191	1, 191	2
192	1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192	14
193	1, 193	2
194	1, 2, 97, 194	4
195	1, 3, 5, 13, 15, 39, 65, 195	8
196	1, 2, 4, 7, 14, 28, 49, 98, 196	9
197	1, 197	2
198	1, 2, 3, 6, 9, 10, 18, 22, 33, 66, 99, 198	12
199	1, 199	2
200	1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200	12

Steps to find the prime factorization with example:

Different steps to find the prime Factorization:

• Even number contains a factor of 2.
• Number which is ending in 5 has a factor of 5.
• Number which is ends with 0 and also it is above 0 contains the factors of 2 and 5.

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Example problem for prime factorization:
Example 1: Find the factorization for the given number 25.
Solution:
25 are divided by 5.
So, 5 are the factors of the given number 25.
Example 2: Find the prime factorization for the given number 28.
Solution:
28 is divided by 2 means, we get 14. Here 14 is not a prime factor. So we factor the 14.
                28 ÷ 2 = 14
14 is divided by 2 means, we get 7. Here 7 is a prime factor.
                14 ÷ 2 = 7
Each factor is a prime number.
So Prime factorization for the given number 28 is 2 × 2 × 7

Example 3: Find the prime factorization of 135
Solution:
             Given
             135
             135 is not a divided by 2. So we divide, 135 can be divided by 3

             135 ÷ 3 = 45

Then we factoring 45, and we find that 3 is the smallest prime number

             45 ÷ 3 = 15

Then we factoring 15, and we find that 3 is the smallest prime number

             15 ÷ 3 = 5

All the factors are prime numbers.

             135 = 3 × 3 × 3 × 5

3 × 3 × 3 × 5 is the prime factorization of 135.

Example 4: Find the prime factorization of 188
Solution:
             Given
             188
             188 can be divided by 2.

             188 ÷ 2 = 94

Then we factoring 94, and we find that 2 is the smallest prime number

             94 ÷ 2 = 47

             47 is a prime number.

All the factors are prime numbers.

             188 = 2 × 2 × 47

2 × 2 × 47 is the prime factorization of 188.