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.

Input

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.
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

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

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

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?

Factorization of 36

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

Factorization table

Number

Factors

Factorization of 4

1,2,4

Factorization of 6

1,2,3,6

Factorization of 8

1,2,4,8

Factorization of 9

1,3,9

Factorization of 10

1,2,5

Factorization of 12

1,2,3,4,6,12

Factorization of 14

1,2,7,14

Factorization of 15

1,3,5,15

Factorization of 16

1,2,4,8,16

Factorization of 18

1,2,3,6,9,18

Factorization of 20

1,2,4,5,10,20

Factorization of 21

1,3,7,21

Factorization of 22

1,2,11,22

Factorization of 24

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

Factorization of 25

1,2,5,25

Factorization of 26

1,2,13,26

Factorization of 27

1,3,9,27

Factorization of 28

1,2,4,7,14,28

Factorization of 30

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

Factorization of 32

1,2,4,8,16,32

Factorization of 33

1,3,11,33

Factorization of 35

1,5,7,35

Factorization of 36

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

Factorization of 38

1,2,19,38

Factorization of 40

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

Factorization of 42

1,2,6,7,21,42

Factorization of 44

1,2,4,11,22,44

Factorization of 45

1,3,5,9,15,45

Factorization of 48

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

Factorization of 49

1,7,49

Factorization of 50

1,2,5,10,25,50

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