Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org

Prime factorization calculator

google play badge app store badge

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.

Prime Factorization Calculator
that shows a step by step explanation
help ↓↓ examples ↓↓
Find prime factorization and factor tree
Find all factors
Find all factor pairs
Check if the number is prime or not

Get Widget Code

working...
EXAMPLES
example 1:ex 1:
Create factor tree for 154 ?
example 2:ex 2:
Find prime factorization of 70 and create factor tree?
example 3:ex 3:
What are the prime factors of 18240 ?
example 4:ex 4:
Find all factor pairs of 548.
example 5:ex 5:
Is the number 1361 prime or composite?
Find more worked-out examples in the database of solved problems..

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
Search our database with more than 250 calculators
440 432 550 solved problems