Prime Factorization Calculator

What is Prime Factorization?

Prime factorization is the decomposition of any number in the multiple of factors and the product of the factors gives the original number.

It is similar to the factoring method, but this process breaks positive numbers/integers into the multiple of prime numbers as its factors. 

For example: the prime factorization of “40 = 2 × 2 × 2 × 5”. 

How to do Prime Factorization?

There are two well-known methods to perform prime factorization and find prime factors of any positive number. Their names are given below:

• Prime factorization by factor tree method
• Prime factorization by trial division method

• Factor Tree Method 

Factor tree method is used to find the prime factors by adjusting factors in a special pattern that looks like a tree. This method starts with the smallest prime number and sets the quotient & divisor on the tree after division. To make an accurate and awesome tree use our prime factors calculator. 

Example: 

Find the prime factor of “48” by using the tree method.

Solution

Step 1: Write the number at the top then draw two branches for the divisor and quotient to construct the tree.

Note whether the given number is prime or not, if prime then leave it, while if not then continue the division process.

Step 2: Factor the numbers and place the quotient or devisor on the branches.

Now, divide the given number and start with “2” because it is even. 

Step 3: Repeat the process until get the prime number or “1”. 

Step 4: In the last, note the prime factors from the outer nodes. 

Now, note the prime factor from nodes and multiply them all together. The node is also known as the leaf node of the factor tree.

48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3

Thus, the prime factors of “48” are “2 & 3”. To verify this result use our above prime number factor calculator.  

• Division Method 

Division method is also used to find prime factors by dividing a number in table form. In this method arrange the numbers in table format and divide by the smallest prime number. To understand how to find the prime factor by division method see the below example.

Example: 

Find the prime factor of “342” by using the trial division method.

Solution:

Step 1: Adjust the number along the division table and start with the smallest prime divisor.

Use the smallest prime number (usually 2) and place the divisor on the left side of the table & quotient in the next row.

Step 2: Continue to divide every new quotient by a suitable prime number, until the quotient becomes “1 or prime number”.

Step 3: Finally, note the prime factors from the division table. 

342 = 2 x 3 x 3 x 19 = 2 x 3² x 19

Thus, the prime factors of “342” are “2, 3, & 19”. However, to find factors instantly use our prime factorization calculator.

FAQ’s

What are prime factors of a number?

The prime factor is the prime divisor of a number and returns the original number when multiplied together. For example, 2 and 3 are the prime factors of “12,” that written as: 12 = 2 × 2 × 3. 

What is the prime number?

Prime number is a positive natural number that is greater than one and has only two positive divisors “1 & itself” such as {2, 3, 5, 7, 11, 13, 17, 19, …}. 

When to use prime factorization?

Prime factorization is one common method that is used to find LCM and GCF of a set of numbers. It is helpful for large numbers where lcm & gcf findings are difficult by listing factors.

How to find prime factors of a number?

Prime factors of any positive number can be found by using the methods of factorization. The manual calculation of these methods is discussed above. But, for a quick solution use our factor calculator.

Can prime factorization calculator handle large numbers?

Yes, our prime number factor calculator is an advanced tool that handles any positive large numbers and finds their prime factors. Our prime factor calculator also provides steps to finding factors of any number.