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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 128625.
solution
The prime factorization of 128625 is:
$$ 128625 = 3\cdot5\cdot5\cdot5\cdot7\cdot7\cdot7 $$Which is the same as :
$$ 128625 = 3\cdot5^{3}\cdot7^{3} $$explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 128625 can be written as 5 × 25725. |
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| 25725 can be written as 5 × 5145. |
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| 5145 can be written as 5 × 1029. |
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| 1029 can be written as 3 × 343. |
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| 343 can be written as 7 × 49. |
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| 49 can be written as 7 × 7. |
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| The end nodes are the prime factors of the number 128625. |
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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.
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60
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10
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6
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Step 2: Write 10 as a product of 2 and 5. $ \color{blue}{10 = 2 \cdot 5} $.
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60
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10
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5
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2
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6
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Step 3: Write 6 as a product of 2 and 3. $ 6 = 2 \cdot 3 $.
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60
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10
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5
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2
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6
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2
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3
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Step 4: The end nodes are the prime factors of 60.
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60
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10
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5
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2
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6
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2
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3
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Finding all factors
Example: Find all factors of 54.
Step 1: Begin the list with 1 and end it with 54.
Step 2: Since $ 54 = 2 \cdot 27 $ we put in 2 and 27 into an array.
Step 3: Since $ 54 = 3 \cdot 18 $ so we will put in 3 and 18 into an array.
Step 4:At the end we have $ 54 = 6 \cdot 9 $
Check if the number is prime
Example: Check whether a number 581 is prime or not.
Step 1: Find the square root of 581.
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.
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.