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**Education Calculators** ▶ Prime Factorization Calculator

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For the ease, the experts from calculator-online provided a simple and tested prime factorization calculator that helps to determine the prime factor of a positive integer. In this post, you will come to know how to find prime factorization of a number and much more!

Well, before knowing about our factorization calculator, you should beware of some terms, read on to know about these terms!

A prime number is said to be an integer or whole number, which contains only two factors – 1 and itself. In another way, a number that can be divided evenly only by 1 and by itself is said to be as a prime number. Prime numbers might also be greater than 1. For e:g – 3 is a prime number as 3 cannot be divided evenly by any numbers except for 1 and 3. However, 6 is not a prime number as it can be divided evenly by 2 or 3. You can utilize prime number calculator to figure out the prime factorization of any numbers.

Composite numbers are also whole numbers, but have at least three factors. Prime numbers only have two factors that are 1 and itself. For example – the only factors for 2 is 1 and 2 (1 x 2). However, 4 is with 3 factors: 1, 2, and 4 (1 x 4 and 2 x 2). If you want to figure out whether a number is prime or composite, then you ought to determine how many factors that number has. Don’t to worry; our online factorize calculator helps to know how many factors a number has.

Let’s move ahead to know the term ‘Prime Factor.’

In simple words, prime factor is indicated as the factor for the given number that is said to be a prime number – factors are said to be as the numbers that multiply together to avail another number. In simple words, prime factor is represents the determining which prime numbers multiply together to get the original number. Our prime factor calculator is works as a natural assistance to figure out the prime factor of any number.

In mathematical terms the prime factorization definition is very simple, prime factorization is also said to be as decomposition or integer factorization. Prime factorization is a simple way that expressing a number as a product of prime numbers. The prime numbers that are used in the product statement are said to be as the prime factors of the number. You can find out the prime factorization of any prime number with the ease of the above prime factorization calculator.

**For Example:**

24 = 2 x 2 x 2 x 3.

The above statement is the prime factorization for the number 24, and the number 2 and 3 are said to be the prime factors of 24.

Our prime factorization calculator is an incredible tool through which you can readily factor positive integers into prime factors. You can be able to find out the prime factors for a number with the ease of this prime factors calculator. Give a read to know more about this hassle-free tool:

It’s very simple, just follow the given step:

- You just have to enter the integer number
- And, hit the calculate button – our calculator shows prime factors of a number, prime decomposition in exponential form, CSV (comma separated values) list of prime factor, and factorization in prime factors tree

Prime factorization is a method of representing a number as a product of prime numbers. Yes, the prime numbers used in the product statement are said to be as the prime factors of the number.

**For Example:**

28 = 2 x 2 x 7: this statement is the prime factorization for the number 28, and the numbers 2 and 7 are the prime factors of 28.

- First, you ought to divide the number by the smallest prime number that divides the number exactly
- If it isn’t exactly divisible by the smallest prime number, then, there is a need to divide the quotient again by the smallest or the next smallest prime number,. You have to repeat the same process again and again until the quotient becomes 1. Make sure that you use only prime numbers to divide
- You ought to multiply all the prime factors, remember that, the product is the number itself

**Example:**

Find the prime factors of 15 by division method:

- 2 is the smallest prime number, but it can’t divide 15 exactly – so, you ought to consider 3
- Now, it is not possible divide 5 by 3, then assume the next smallest prime number 5

The prime factors of 15 are 3 × 5.

Let’s suppose, you have to figure out the prime factors of 16 using a factor tree method:

- First of all, you have to consider the number 16 as the root of the tree
- Then, you ought to write the pair of factors as the branches of the tree, i:e, 2 × 8 = 16
- You can further factorize the composite factor 8 as 4 and 2, and again the composite factors 4 as 2 and 2

You ought to repeat the same process again till you get the prime factors of all the composite factors:

2 × 8 = 16

2 × 4 × 2 = 16

2 × 2 × 2 × 2 = 16

You can utilize the above factor tree calculator to determine the prime factorization trees of a number.

**Prime factorization of 2:**

2 is a prime number

**Prime factorization of 3:**

3 is a prime number

**Prime factorization of 4:**

2 x 2

**Prime factorization of 5:**

5 is a prime number

**Prime factorization of 6:**

2 x 3

**Prime factorization of 7:**

7 is a prime number

**Prime factorization of 8:**

2 x 2 x 2

**Prime factorization of 9:**

3 x 3

**Prime factorization of 10:**

2 x 5

**Prime factorization of 11:**

11 is a prime number

**Prime factorization of 12:**

2 x 2 x 3

**Prime factorization of 13:**

13 is a prime number

**Prime factorization of 14:**

2 x 7

**Prime factorization of 15:**

3 x 5

**Prime factorization of 16:**

2 x 2 x 2 x 2

**Prime factorization of 17:**

17 is a prime number

**Prime factorization of 18:**

2 x 3 x 3

**Prime factorization of 19:**

19 is a prime number

**Prime factorization of 20:**

2 x 2 x 5

**Prime factorization of 21:**

3 x 7

**Prime factorization of 22:**

2 x 11

**Prime factorization of 23:**

23 is a prime number

**Prime factorization of 24:**

2 x 2 x 2 x 3

**Prime factorization of 25:**

5 x 5

**Prime factorization of 26:**

2 x 13

**Prime factorization of 27:**

3 x 3 x 3

**Prime factorization of 28:**

2 x 2 x 7

**Prime factorization of 29:**

29 is a prime number

**Prime factorization of 30:**

2 x 3 x 5

**Prime factorization of 31:**

31 is a prime number

**Prime factorization of 32:**

2 x 2 x 2 x 2 x 2

**Prime factorization of 33:**

3 x 11

**Prime factorization of 34:**

2 x 17

**Prime factorization of 35:**

5 x 7

**Prime factorization of 36:**

2 x 2 x 3 x 3

**Prime factorization of 37:**

37 is a prime number

**Prime factorization of 38:**

2 x 19

**Prime factorization of 39:**

3 x 13

**Prime factorization of 40:**

2 x 2 x 2 x 5

**Prime factorization of 41:**

41 is a prime number

**Prime factorization of 42:**

2 x 3 x 7

**Prime factorization of 43:**

43 is a prime number

**Prime factorization of 44:**

2 x 2 x 11

**Prime factorization of 45:**

3 x 3 x 5

**Prime factorization of 46:**

2 x 23

**Prime factorization of 47:**

47 is a prime number

**Prime factorization of 48:**

2 x 2 x 2 x 2 x 3

**Prime factorization of 49:**

7 x 7

**Prime factorization of 50:**

2 x 5 x 5

**Prime factorization of 51:**

3 x 17

**Prime factorization of 52:**

2 x 2 x 13

**Prime factorization of 53:**

53 is a prime number

**Prime factorization of 54:**

2 x 3 x 3 x 3

**Prime factorization of 55:**

5 x 11

**Prime factorization of 56:**

2 x 2 x 2 x 7

**Prime factorization of 57:**

3 x 19

**Prime factorization of 58:**

2 x 29

**Prime factorization of 59:**

59 is a prime number

**Prime factorization of 60:**

2 x 2 x 3 x 5

**Prime factorization of 61:**

61 is a prime number

**Prime factorization of 62:**

2 x 31

**Prime factorization of 63:**

3 x 3 x 7

**Prime factorization of 64:**

2 x 2 x 2 x 2 x 2 x 2

**Prime factorization of 65:**

5 x 13

**Prime factorization of 66:**

2 x 3 x 11

**Prime factorization of 67:**

67 is a prime number

**Prime factorization of 68:**

2 x 2 x 17

**Prime factorization of 69:**

3 x 23

**Prime factorization of 70:**

2 x 5 x 7

**Prime factorization of 71:**

71 is a prime number

**Prime factorization of 72:**

2 x 2 x 2 x 3 x 3

**Prime factorization of 73:**

73 is a prime number

**Prime factorization of 74:**

2 x 37

**Prime factorization of 75:**

3 x 5 x 5

**Prime factorization of 76:**

2 x 2 x 19

**Prime factorization of 77:**

7 x 11

**Prime factorization of 78:**

2 x 3 x 13

**Prime factorization of 79:**

79 is a prime number

**Prime factorization of 80:**

2 x 2 x 2 x 2 x 5

**Prime factorization of 81:**

3 x 3 x 3 x 3

**Prime factorization of 82:**

2 x 41

**Prime factorization of 83:**

83 is a prime number

**Prime factorization of 84:**

2 x 2 x 3 x 7

**Prime factorization of 85:**

5 x 17

**Prime factorization of 86:**

2 x 43

**Prime factorization of 87:**

3 x 29

**Prime factorization of 88:**

2 x 2 x 2 x 11

**Prime factorization of 89:**

89 is a prime number

**Prime factorization of 90:**

2 x 3 x 3 x 5

**Prime factorization of 91:**

7 x 13

**Prime factorization of 92:**

2 x 2 x 23

**Prime factorization of 93:**

3 x 31

**Prime factorization of 94:**

2 x 47

**Prime factorization of 95:**

5 x 19

**Prime factorization of 96:**

2 x 2 x 2 x 2 x 2 x 3

**Prime factorization of 97:**

97 is a prime number

**Prime factorization of 98:**

2 x 7 x 7

**Prime factorization of 99:**

3 x 3 x 11

**Prime factorization of 100:**

2 x 2 x 5 x 5