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Prime Factorization Calculator

Prime factorization calculator

This calculator finds the prime factorization of a given number and creates a factor tree. Also, the calculator finds all factors, all factor pairs, and can check if the number is prime or not. The calculator generates a step-by-step explanation of how the work was done.

Find the prime factorization of number 2048.

solution

The prime factorization of 2048 is:

$$ 2048 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2 $$

Which is the same as :

$$ 2048 = 2^{11} $$

explanation

Prime factorization can be nicely visualized by creating a factorization tree.

2048 can be written as 2 × 1024.	2048 2 1024
1024 can be written as 2 × 512.	2048 2 1024 512 2
512 can be written as 2 × 256.	2048 2 1024 512 2 256 2
256 can be written as 2 × 128.	2048 2 1024 512 2 256 128 2 2
128 can be written as 2 × 64.	2048 2 1024 512 2 256 128 2 64 2 2
64 can be written as 2 × 32.	2048 2 1024 512 2 256 128 2 64 32 2 2 2
32 can be written as 2 × 16.	2048 2 1024 512 2 256 128 2 64 32 2 16 2 2 2
16 can be written as 2 × 8.	2048 2 1024 512 2 256 128 2 64 32 2 16 8 2 2 2 2
8 can be written as 2 × 4.	2048 2 1024 512 2 256 128 2 64 32 2 16 8 2 4 2 2 2 2
4 can be written as 2 × 2.	2048 2 1024 512 2 256 128 2 64 32 2 16 8 2 4 2 2 2 2 2 2
The end nodes are the prime factors of the number 2048.	2048 2 1024 512 2 256 128 2 64 32 2 16 8 2 4 2 2 2 2 2 2

Prime Factorization Calculator

that shows a step-by-step explanation
help ↓↓ examples ↓↓ tutorial ↓↓

Input integer number:

Select what to compute:

Find prime factorization

Find all factors

Find all factor pairs

Check if the number is prime or not

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Examples

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ex 2:

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ex 5:

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What is prime factorization?

Prime factorization is a process of finding the group of prime numbers such that when multiplied together, they give the original number. For example, the prime factorization of 15 is 5 * 3, because 5 and 3 are both prime numbers that when multiplied together yield 15. This calculator computes prime factorization and factor trees for every integer up to 21474836460000.

Find the prime factorization and factor tree for 60.

Step 1: Start with any number that divides 60; for our example, we will select 10.

60
- 10
- 6

Step 2: Write 10 as a product of 2 and 5. $ \color{blue}{10 = 2 \cdot 5} $.

60
- 10
  - 5
  - 2
- 6

Step 3: Write 6 as a product of 2 and 3. $ 6 = 2 \cdot 3 $.

60
- 10
  - 5
  - 2
- 6
  - 2
  - 3

Step 4: The end nodes are the prime factors of 60.

60
- 10
  - 5
  - 2
- 6
  - 2
  - 3

$$ 60 = 2 \cdot 2 \cdot 3 \cdot 5 $$

Finding all factors

Example: Find all factors of 54.

Step 1: Begin the list with 1 and end it with 54.

$$ \color{blue}{\boxed{1}} ~ , ~ . ~ . ~ . ~ , ~ \color{blue}{\boxed{54}} $$

Step 2: Since $ 54 = 2 \cdot 27 $ we put in 2 and 27 into an array.

$$ 1 ~ , ~ \color{blue}{\boxed{2}} ~ , ~ . ~ . ~ . ~ , ~ \color{blue}{\boxed{27}} ~ , ~ 54 $$

Step 3: Since $ 54 = 3 \cdot 18 $ so we will put in 3 and 18 into an array.

$$ 1 ~ , ~ 2, ~ \color{blue}{\boxed{3}} ~ , ~ . ~ . ~ . ~ , ~ \color{blue}{\boxed{18}} ~ , ~ 27 ~ , ~ 54 $$

Step 4:At the end we have $ 54 = 6 \cdot 9 $

$$ 1 ~ , ~ 2 ~ , ~ 3 ~ , ~ \color{blue}{\boxed{6}} ~ , ~ \color{blue}{\boxed{9}} ~ , ~ 18 ~ , ~ 27 ~ , ~ 54 $$

Check if the number is prime

Example: Check whether a number 581 is prime or not.

Step 1: Find the square root of 581.

$$ \sqrt{581} = 24.1 \approx = 25$$

Step 2: Try to divide 581 by all prime numbers less or equal to 25.

In this example we will try to divide 581 with :
2 , 3, 5, 7, 11, 13, 17, 19 and 23.

$$ \begin{aligned} 581 : 2 & = 290.5 \\ 581 : 3 & = 484 \\ 581 : 5 &= 116.2 \\ 581 : 7 &= 83 \end{aligned} $$

581 is divisible by 3 so is is not prime.

RESOURCES

1. Prime Factorization - video tutorial

2. Prime Factorization : Definition, Methods, Examples, FAQs

3. Prime Factorization test with video solutuins.

4. Print all prime factors - code in C++, C, Java, Python, C#, Javascript and PHP.

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