# Prime Factorization and Factorization

## Find the Prime factor, Factor and Factor Pairs for a given number

HomeMath

Prime Factor

You can input a number and find the prime factor, factor and factor pair.

Prime Factorization: 2 * 2 * 3

Factors: 1, 2, 3, 4, 6, 12

Factor Pairs : (1,12),(2,6),(3,4)

## What is Prime Factorization?

• Prime factorization is the method for finding prime factors of a composite number. There is a theorem that states: Any integer greater than one can be uniquely written as product of prime numbers.

• Prime factor example

Let's take 6. It can be written as 2 x 3 which is nothing but the multiplication of two prime numbers.
find the prime factorization for 124. 124 = 2 * 2 * 31 , Here all the three factors are prime and the prime factorization of 124 is 22 x 31

## How to Factorize a number?

• Step 1: As we discussed about integers, we clearly notice that all integers can be written as Multiplication of two numbers. Even we can write prime number in this way.(1 x prime.no).

• Step 2: Lets take a number xy.Try to write in multiplication of two numbers. (i.e) x * y.

• Step 3: Next is to check whether the number x and y can be written as multiplication of two numbers.We need to repeat this step until the number reaches to prime number.

• Example: Factorization of 36

Step 1: Express it as multiplication of two number. 36 = 12 x 3
Step 2: We can write 12 as multiplication of two numbers, 12 = 4 x 3 , 12 = 6 x 2.
Step 3: 4 and 6 can be written as 2 x 2 and 2 x 3 respectively.
Now collect the numbers and we can ignore the duplicate numbers. So now the factors of 12 are >2, 3, 4, 6

## Factor Tree

• What is Factor tree? Factor tree is an another way of finding the prime factors of a given number. In this method, we split the given number into two branches and again split the numbers in the branches to two numbers. Repeat this process , until the split number is a prime.

• Factor tree of 36 is 2x2 x 3x3 First we split 36 into 9 x 4. And in each branch we have composite so our aim is to split all branch element to multiples of prime numbers.So split 9 as 3 x 3 and 4 as 2 x 2 respectively in the branch. Now at the end node all the numbers are prime numbers.So the factorization of 36 is 2 x 2 3 x 3.

## Factorization table

Factorization of Number Factors
4 1,2,4
6 1,2,3,6
8 1,2,4,8
9 1,3,9
10 1,2,5
12 1,2,3,4,6,12
14 1,2,7,14
15 1,3,5,15
16 1,2,4,8,16
18 1,2,3,6,9,18
20 1,2,4,5,10,20
21 1,3,7,21
22 1,2,11,22
24 1,2,3,4,6,8,12,24
25 1,2,5,25
26 1,2,13,26
27 1,3,9,27
28 1,2,4,7,14,28
30 1,2,3,5,6,10,15,30
32 1,2,4,8,16,32
33 1,3,11,33
35 1,5,7,35
36 1,2,3,4,6,9,12,36
38 1,2,19,38
40 1,2,4,5,8,10,20,40
42 1,2,6,7,21,42
44 1,2,4,11,22,44
45 1,3,5,9,15,45
48 1,2,3,4,6,8,12,16,48
49 1,7,49
50 1,2,5,10,25,50
51 1,3,17,51
52 1,2,4,13,26,52
54 1,2,3,6,9,27,54
55 1,5,11,55
56 1,2,4,7,8,14,28,56
60 1,2,3,4,5,6,10,12,15,20,30,60
63 1,3,7,9
64 1,2,4,8,32,64
65 1,5,13,65
66 1,2,3,6,11,22,33,66
68 1,2,4,7,17,34,64
70 1,2,5,7,10,70
72 1,2,3,4,6,8,12,18,36,72
75 1,3,5,15,25,75
76 1,2,4,19,38,76
77 1,7,11,77
80 1,2,4,5,8,10,16,20,40,80
81 1,3,9,27,81
84 1,2,3,4,6,7,12,21,42,84
85 1,5,17,85
88 1,2,4,8,11,22,44,88
90 1,2,3,5,6,9,15,30,45,90
91 1,7,13,91
96 1,2,3,4,6,8,12,16,24,32,48,96
98 1,2,7,14,49,98
99 1,3,9,11,33,99
100 1,2,4,5,10,20,25.50,100
105 1,3,5,7,15,21,35,105
108 1,2,3,4,6,9,12,18,27,36,54,108
110 1,2,5,10,11,22,55,110
112 1,2,4,7,8,14,16,28,56,112
120 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
125 1,5,25,125
128 1,2,4,8,16,32,64,128
140 1,2,4,5,7,10,14,20,28,35,70,140
144 1,2,3,4,6,8,9,12,16,18,24,36,48,72,144
147 1,3,7,21,49,147
150 1,2,3,5,6,10,15,25,30,50,75,150
180 1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
196 1,2,4,7,14,28,49,98,196
200 1,2,4,5,8,10,20,25,40,50,100,200
210 1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
240 1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240
245 1,5,7,35,49,245
300 1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300
360 1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360

## Prime Factorization table

Number Prime Factors Prime Factorization
4 2 2 * 2
6 2,3 2 * 3
8 2 2 * 2 * 2
9 3 3 * 3
10 2,5 2 * 5
12 2,3 2 * 2 * 3
14 2,7 2 * 7
15 3,5 3 * 5
16 2 2 * 2 * 2 * 2
18 2,3 2 * 3 * 3
20 2,5 2 * 2 * 5
21 3,7 3 * 7
22 2,11 2 * 11
24 2,3 2 * 2 * 2 * 3
25 2,5 5 * 5
26 2,13 2 * 13
27 3 3 * 3 * 3
28 2,7 2 * 2 * 7
30 2,3,5 2 * 3 * 5
32 2 2 * 2 * 2 * 2 * 2
33 3,11 3 * 11
35 5,7 5 * 7
36 2,3 2 * 2 * 3 * 3
38 2,19 2 * 19
40 2,5 2 * 2 * 2 * 5
42 2,7 2 * 3 * 7
44 2,11 2 * 2 * 11
45 3,5 3 * 3 * 5
48 2,3 2 * 2 * 2 * 2 * 3
49 7 7 * 7
50 2,5 2 * 5 * 5
51 3,17 3 * 17
52 2,13 2 * 2 * 13
54 2,3 2 * 3 * 3 * 3
55 5,11 5 * 11
56 2,7 2 * 2 * 2 * 7
60 2,3,5 2 * 2 * 3 * 5
63 3,7 3 * 3 * 7
64 2 2 * 2 * 2 * 2 * 2 * 2
65 5,13 5 * 13
66 2,3,11 2 * 3 * 11
68 2,7 2 * 2 * 17
70 2,5,7 2 * 5 * 7
72 2,3 2 * 2 * 2 * 3 * 3
75 3,5 3 * 5 * 5
76 2,19 2 * 2 * 19
77 7,11 7 * 11
80 2,5 2 * 2 * 2 * 2 * 5
81 3 3 * 3 * 3 * 3
84 2,3,7 2 * 2 * 3 * 7
85 5,17 5 * 17
88 2,11 2 * 2 * 2 * 11
90 2,3,5 2 * 3 * 3 * 5
91 7,13 7 * 13
96 2,3 2 * 2 * 2 * 2 * 2 * 3
98 2,7 2 * 7 * 7
99 3,11 3 * 3 * 11
100 2,5 2 * 2 * 5 * 5
105 3,5,7 3 * 5 * 7
108 2,3 2 * 2 * 3 * 3 * 3
110 2,5,11 2 * 5 * 11
112 2,7 2 * 2 * 2 * 2 * 7
120 2,3,5 2 * 2 * 2 * 3 * 5
125 5 5 * 5 * 5
128 2 2 * 2 * 2 * 2 * 2 * 2 * 2
140 2,5,7 2 * 2 * 5 * 7
144 2,3 2 * 2 * 2 * 2 * 3 * 3
147 3,7 3 * 7 * 7
150 2,3,5 2 * 3 * 5 * 5
180 2,3,5 2 * 2 * 3 * 3 * 5
196 2,7 2 * 2 * 7 * 7
200 2,5 2 * 2 * 2 * 5 * 5
210 2,3,5,7 2 * 3 * 5 * 7
240 2,3,5 2 * 2 * 2 * 2 * 3 * 5
245 5,7 5 * 7 * 7
300 2,3,5 2 * 2 * 3 * 5 * 5
360 2,3,5 2 * 2 * 2 * 3 * 3 * 5

## Frequently Asked Questions on Prime Factorization

• Factorization is the method of breaking the numbers into the factors.
For example: 36 = 4 x 9
Prime factorization is the method of breaking down the numbers to the prime factors.

For example: 36 = 22 x 32

• Every integer greater can be written as multiplication of prime factors.
There will be many factors for a number.
In that the bigger number is a largest prime factor.
For example : Prime factors of 30 is 2 , 3 and 5.
In the factors list 5 is the biggest one so 5 is the greatest prime factor of 30.

• The smallest nunber among all the prime factors of the number is the least / lowest prime factor ?
For example : Prime factors of 30 is 2 , 3 and 5.
In the factors list 2 is the smallest one so 5 is the lowest prime factor of 30.

• Factor tree is an another way of finding the prime factors of a given number.
In this method we split the given number into two branches and again splits the numbers in the branches to two numbers.
Repeat this process , untill the splitten number is a prime.

• Lets take 30 as an example, 30 can be written as 6 x 5 since 6 is not a prime so split 6 into 2 x 3 .
Now all the three factors are prime. And prime factors of 30 are 2 , 3 , and 5.

• Prime factorization of 100:

22 x 52

• Factor tree , Long division methods , and Grouping method.