Prime Factorization Calculator

How to use the Prime factorization calculator?

This tool works when you

1. Enter the number.
2. Click “Go” or press enter.

Well, that is all you need to do. You can enter a number between 1 and 100000000 which is ten crores. You can use the numbers to word converter for such conversions.

What are prime numbers?

The simplest definition of prime numbers will be:

        “The whole numbers which have only two multiples; one and itself.”

These numbers do not include 0 (not a natural number) and 1 (only one multiple). 

The opposite concept of prime numbers is composite numbers. These are the numbers that have more than 2 factors.

Fun fact: You can use the prime factors calculator as a prime number calculator because if the number you entered is a prime number, the result will be the same number.

What is prime factorization?

According to the fundamental theorem of arithmetics, whole numbers are either prime numbers or such numbers that are a product of prime numbers.

The process of breaking these composite numbers into a set of prime numbers is called prime factorization. 

Prime factorization is used for finding LCM as well. The highest power factors of two or more numbers are multiplied to know the least common multiple.

Their famous methods for prime factorization are trial division, prime factor tree, and well, our calculator ;).

How to do prime factorization?

Under this heading, we will have a detailed look at the methods of solving prime factorization.

Trial division:

It’s a time taking and tedious method. But on the other hand, it is easy to understand. In this method, you divide the value in question by prime numbers for a whole quotient.

The process is carried out until both the divisor and the quotient are prime numbers and no more division is eventually possible.

Example:

Assume you want to find the prime factors for the number 342.

We will start with the first prime number that is two. The question arises “Is 342 divisible by 2?” Yes because it is an even number. 

342 / 2 = 171

Let’s see if it is again divisible by 2. The answer is no as it is an odd number and the quotient will be a decimal value (i.e 85.5). That means we move on to the next prime number, 3.

171 / 3 = 57

It is possible to divide it by 3 again.

57 / 3 = 19

Since 19 itself is a prime number, that means we have found all of the prime factors for 342. 

So, 342 = 2 x 3 x 3 x 19.  

Note: There is only one possible set of prime factors for a particular number. The arrangement of the factors does not matter.

Prime factor tree:

This method also goes by the name prime decomposition. It is somewhat similar to the previous method. While forming a factor tree, you break the number into any possible factors whether prime or not.  

But it should be kept in mind that the end results must comprise prime numbers only. 

Example:

Perform prime factorization for 72. Use the factor tree method.

Solution:

Step 1: Divide 72 by 2.

Step 2: Divide 36.

Step 3: Keep on breaking into factors.

As you can see both last factors are prime numbers. The factor tree ends here. Hence;

72 = 2 x 2 x 2 x 3 x 3 it can also be written as = 23 x 32.

Prime factorization chart:

Below is a detailed list of prime factors of numbers 1 to 50.

Number	Factors	Prime Factors
1	1
2	1, 2	2
3	1, 3	3
4	1, 2, 4	2 x 2
5	1,5	5
6	1, 2, 3, 6	2 x 3
7	1, 7	7
8	1, 2, 4, 8	2 x 2 x 2
9	1, 3, 9	3 x 3
10	1, 2, 5, 10	2 x 5
11	1, 11	11
12	1, 2, 3, 4, 6, 12	2 x 2 x 3
13	1, 13	13
14	1, 2, 7, 14	2 x 7
15	1, 3, 5, 15	3 x 5
16	1, 2, 4, 8, 16	2 x 2 x 2 x 2
17	1, 17	17
18	1, 2, 3, 6, 9, 18	2 x 3 x 3
19	1, 19	19
20	1, 2, 4, 5, 10, 20	2 x 2 x 5
21	1, 3, 7, 21	3 x 7
22	1, 2, 11, 22	2 x 11
23	1, 23	23
24	1, 2, 3, 4, 6, 8, 12, 24	2 x 2 x 2 x 3
25	1, 5, 25	5 x 5
26	1, 2, 13, 26	2 x 13
27	1, 3, 9, 27	3 x 3 x 3
28	1, 2, 4, 7, 14, 28	2 x 2 x 7
29	1, 29	29
30	1, 2, 3, 5, 6, 10, 15, 30	2 x 3 x 5
31	1, 31	31
32	1, 2, 4, 8, 16, 32	2 x 2 x 2 x 2 x 2
33	1, 3, 11, 33	3 x 11
34	1, 2, 17, 34	2 x 17
35	1, 5, 7, 35	5 x 7
36	1, 2, 3, 4, 6, 9, 12, 18, 36	2 x 2 x 3 x 3
37	1, 37	37
38	1, 2, 19, 38	2 x 19
39	1, 3, 13, 39	3 x 13
40	1, 2, 4, 5, 8, 10, 20, 40	2 x 2 x 2 x 5
41	1, 41	41
42	1, 2, 3, 6, 7, 14, 21, 42	2 x 3 x 7
43	1, 43	43
44	1, 2, 4, 11, 22, 44	2 x 2 x 11
45	1, 3, 5, 9, 15, 45	3 x 3 x 5
46	1, 2, 23, 46	2 x 23
47	1, 47	47
48	1, 2, 3, 4, 6, 8, 12, 16, 24, 48	2 x 2 x 2 x 2 x 3
49	1, 7, 49	7 x 7
50	1, 2, 5, 10, 25, 50	2 x 5 x 5