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# Prime Factorization Calculator + Online Solver With Free Steps

The **Prime Factorization Calculator** is a free online tool for dividing an integer into prime numbers that multiply to obtain the original value.

The term “**Prime Decomposition**” also applies to this. Natural numbers that are bigger than One and cannot be generated by simply multiplying smaller integers are called prime numbers.

Prime numbers are entirely positive whole numbers, which can occasionally contain Zero in some interpretations. The number seven illustrates a prime number because it can only be created by multiplying the **digits 1 and 7**. There are further examples** 3, 11, etc.**

## What Is a Prime Factorization Calculator?

**The Prime Factorization Calculator is an online calculator that determines all of an integer number’s prime factors.**

**The process used to identify an integer’s prime factors is known as prime factorization.** The original integer can be determined by multiplying the integers’ prime factors. As far as we know, a prime number can be both 1 and the integer.

The **building blocks of all numbers are said to be the prime numbers.** The whole number is divided into prime factors using a technique known as prime factorization.

## How To Use a Prime Factorization Calculator?

You can use the **Prime Factorization Calculator** by following the detailed procedure below. The calculator can provide you with the desired results in seconds.

To get the **Prime Factors** of the given integers, follow the steps below.

### Step 1

Fill in the provided input box with the **integer**.

### Step 2

To calculate the** Prime Factors** for the provided data and to view the complete, step-by-step solution for the **Prime Factors** Calculation, click the **“Find Prime Factors”** button.

## How Does a Prime Factorization Calculator Work?

The **Prime Factorization Calculator** works by dividing a composite integer into prime number products. Factoring algorithms come in a variety, with some being more complex than others.

### Prime Factor

**A group of prime numbers that, when combined, equals the number is said to be an integer prime factor.**

**A prime number is one that can only be divided by one and on its own.**

Finding all of a number’s prime factors is the process of **Prime Factorization**. To achieve this, keep breaking the number down into smaller pieces, then divide those parts again into smaller parts until none of the details can be broken down any further.

### Trial Division

Finding all of a number’s prime factors is the process of prime factorization. To achieve this, keep breaking the number down into smaller pieces, then divide those parts again into smaller parts until none of the parts can be broken down any further.

\[ \frac{820}{2} = 410 \]

\[ \frac{410}{2} = 205 \]

Try the subsequent integers since 205 is no more divisible by the number 2. 3 cannot accurately reduce 205; The number four is not a prime number. However, it is divisible by 5:

\[ \frac{205}{5} = 41 \]

This brings the trial division to a close because 41 is a prime number. Thus:

**820 = 41 x 5 x 2 x 2 **

The values may alternatively be written as follows:

**820 = 41 x 5 x 2$^2$**

Although 820 is a simple case, the “brute force” approach of finding a number’s prime factors may rapidly become laborious.

This algorithm is not at all practical, its worst. It can be very time- and resource-intensive.

There are other methods, but conceptually we’ll stick with this one: you’ll quickly grasp how to determine the prime decomposition without paying attention to more theoretical or difficult arithmetic.

### Prime Decomposition

Prime decomposition, which is another typical method of prime factorization, may require the utilization of a factor tree. You can create a factor tree by dissecting the composite integer into its factors until all of the integers are prime.

To get the prime factors in the case below, reduce 820 by the prime factor 2, then keep reducing the resulting number until all factors are prime. The scenario below illustrates two methods for developing a factor tree using the integer 820.

### Prime Factorization of Highest Common Multiple and Least Common Multiple

Composite numbers are produced by multiplying the prime factors by any positive integer or whole number. In order to factorize the compound numbers and identify their prime factors, prime factorization is essentially used.

The LCM and HCF of any specified collection of integers are also determined using this method.

The largest common factor between any two digits is known as the highest common factor, and the lowest common multiple between any two digits is known as the least common multiple.

### List of Prime Factors Under 300

2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 |

31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 |

73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 |

127 | 131 | 137 | 139 | 149 | 151 | 157 | 163 | 167 | 173 |

179 | 181 | 191 | 193 | 197 | 199 | 211 | 223 | 227 | 229 |

233 | 239 | 241 | 251 | 257 | 263 | 269 | 271 | 277 | 281 |

283 | 293 |

## Solved Examples

Let’s solve some examples. To better understand the working of the Prime Factorization Calculator.

### Example 1

Show the prime factors of some ordinary integers.

### Solution

The prime factorizations of a few popular numbers are listed below.

2’s prime factors: a prime number

3 factored by primes: prime number

4’s primary factors are: 2$ ^2$

5 factored by primes: prime number

6’s prime factors are 2 and 3.

7 factored by primes: prime number

8’s primary factors are: 2 $^3$

9’s prime factors are: 3$^2$

10’s prime factors are 2 x 5.

11 factored by primes: prime number

12’s prime factors are: 2$^2$ x 3.

13 factored by primes: prime number

14’s prime factors are 2 and 7.

15’s prime factorization is 3 x 5.

16’s prime factorization is 2 $^4$.

17’s prime factors: a prime number

18’s prime factorization is 2 x 32.

19’s prime factors: a prime number

20’s prime factors are 2$^2$ x 5.

21’s prime factorization is 3 x 7.

22’s prime factors are 2 x 11.

23 factored by primes: prime number

24’s prime factorization is 23 x 3.

25’s prime factorization is 5$^2$.

26’s prime factorization is 2 x 13.

27’s prime factorization is 3$^3$.

28’s prime factorization is 22 x 7.

29 factored by primes: prime number

30’s prime factorization is 2 x 3 x 5.

Prime factors that make up the number 31

32’s prime factorization is 2$^5$.

### Example 2

Determine the Prime Factorization of integer ‘75.’

### Solution

We’ll begin with number 2.

Check to see if 75 is divided by 2.

Please switch to the next prime number as it cannot be divided by 2.

3 is the second prime number.

Check to see if 75 can be divided by 3.

Divide 75 by 3 as it is a divisible number.

\[ \frac{75}{3} = 25 \]

Check to see if 25 can be divided by 3.

Please switch to the subsequent prime number as it is not divisible.

5 is the third prime number.

Check to see if 25 can be divided by 5.

Divide by 5 since it is divisible by 25.

\[ \frac{25}{5} = 5 \]

The only factor for the prime number 5 is 1.

\[ \frac{5}{5} = 1 \]

We have finished because we have 1 now.

Just note the prime factorization after counting the occurrences of the divisors:

**75 = 3 x 5$^2$**

### Example 3

Determine the Prime Factorization of integer ‘57.’

### Solution

We’ll start with number two.

Check to see if 57 can be divided by integer 2.

Please switch the following prime number as it is not divisible.

3 is the second prime number.

Check to see if 57 can be divided by 3.

Divide 57 by 3 since it is divisible:

\[ \frac{57}{3} = 19 \]

Other than 1 and 19, there are no factors for the prime number 19:

\[ \frac{19}{19} = 1 \]

We have finished because we have 1 now.

Just tally the divisors’ occurrences (the green numbers) to get their prime factorization:

**57 = 3 x 19**