What is prime factorization?

Prime Factorization is the technique through which we can find the prime numbers that gives us original number on multiplication. For example, if the original number is 12 then by prime factorization we can find prime number that will make number 12 on multiplication. We have to follow some simple steps below:

  • 12 is the original number.
  • In the first step we have to divide number 12 by the smallest prime number.
  • Smallest prime number is 2 therefore we can divide 12 by 2 and it will give us 6.
  • Now 6 is not the prime number and according to definition we have to fine prime numbers so we will divide 6 further. 6 divided by 2 will give us 3 that is the prime number. So we have the answer that is 2 multiplied by 2 that is equal to 4 and 4 multiplied by 3 is equals to 12. Therefore, we can say that 2 2 3 are the factors of 12.

This is the process of manual calculation that might be time taking. To save the time and avoid the mistake you can use prime factor calculator to find the prime factors of any given number.

Also, you can try to learn number system in hindi

What is prime number?

A prime number is the whole number which is greater than 1 and cannot be formed by multiplying different whole numbers. Prime numbers is the figures that are widely used in number theory because of the fundamental theorem of arithmetic. The theorem depicts that the natural numbers greater than 1 are either prime, or even can be simply factored as a product of prime numbers. Remember that prime factorization is the decomposition of a composite number into a product of prime numbers, so you can try the product of prime factors calculator to find the product of prime numbers. Read on!

For example, 2 is the first prime number which cannot be resulted by multiplying any whole numbers. In the same way 3, 11, 19 are some other prime numbers. Whereas factors referred to the numbers that gives us another number by multiplication. For example, 2 multiplied by 3 gives 6 therefore we can say that 2 and 3 are the factors of 6.

In case of some complex numbers it might be difficult to find the factors but prime number calculator is the best option to solve such a task and to get factors of any number immediately without any mistake in the blink of an eye.

Difference between the term Prime numbers & composite numbers:

Prime number is the term which refers to all those numbers that cannot be made by multiplying different whole numbers such as 11, 13, 17 and many more whereas composite numbers can be formed by multiplying different whole numbers such as 4 is the composite number that is the result of 2 multiplied by 2. In the same way 9 is another composite number that is the result of 3 multiplied by 3. On the other hand, 2 and 3 are the prime numbers.

What is a prime factor?

A prime factor is basically a prime number. Any number has its prime factors which gives us original number on multiplication. For example, 3 and 5 are the prime factors of 15 because 3 and 5 are prime numbers and 3 multiplied by 5 is equals to 15. Simply, plug in the integer value into the designated field of prime factorization calculator to find the list of all prime numbers corresponding to the given integer.

How do you find the prime factorization of a Number?

Prime factorization to find prime factors of any number can be done by following methods manually.

Prime factorization trees or Factor Tree Method:

This technique gives demonstrations of all the prime factors of any composite number in a “tree-shape” form. Making factor trees is a good way of doing prime factorization that displays all the factors in a simple form. Use of prime factor tree calculator might be very helpful and time saving for this purpose.

Prime Decomposition: Factors and Exponents: (or Prime decomposition):

Finding prime factors of any number also recognized as prime decomposition. The procedure is same as described above for the prime factorization. However, in the method we can write prime factors as exponents. For example, in case of 50 we have 2 5 and 5. In form of exponents it will be 2 multiplied by 52. the 2 on 5 is known as exponent. Prime factorization calculator has the ability to display exponents of factors so that you can handle your calculation without any error.

Prime Factorization by Trial Division or (Divisibility test or Division Method):

In this method if you have to find the prime factors of 50 then you have to start by checking each integer that how often it will divide 50. The subsequent set will be of prime factors that will give us 50 on multiplication. However, calculation might get long in this way so you can use factored form calculator for your convenience.


2 multiplied by 5 and 5 multiplied by 5 again will give us 50 so the prime factors of 50 are 2 ,5 and 5. In the simplest way you can do following procedure:

  • 50/2 = 25
  • 25/5 = 5
  • 5/5 = 1

Well, the authorized platform of calculator-online provides the simple, but highly accurate calculator that helps you to convert any number into standard form.

FAQ’s (Prime Factorization & Prime Numbers):

What is the prime factorization of 2020?

The prime factorization of 2020 is:

2^2 × 5 × 101

As it has a total of 4 prime factors, 2020 is said to be as a composite number.

What are the prime factors of 5?

Since, 5 is a prime number, so the prime factors of 5 are 1 and 5.

What are the factors of 2020?

The answer is: Factors of 2020 are represented in such a way: 1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010.

Why is 9 not a prime number?

When it comes to 9 to be a prime number, you can see that 9 have only two divisors i: e itself and only 1. However, 9 is also referred to as a semi-prime (also referred to as biprime or 2-almost-prime) as it is the product of a two non-necessarily distinct prime factors. Indeed, 9 = 3 x 3,where 3 is said to be a prime number.

What is the fifth prime number?

Remember that if a number has more than two factors, then it is said to be as a composite number. Well, let’s take a look at first few prime numbers: 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, etc.

Do odd numbers have factors?

A factor is refers to a number that divides into another number exactly and without leaving a remainder. Typically, most numbers contain an even number of factors; however, a square number consists of an odd number of factors. A prime number only has two factors, the number itself and 1.

What is least factor of a number?

The least prime factor of an integer n is said to be as the smallest prime number, which divides the number.

Why 1 is not a prime number?

According to the evidence-based study, the definition of a prime number reveals that prime number is a positive integer that has exactly two positive divisors. However, 1 only contains one positive divisor i:e 1 itself, so that’s the reason why it is not said to be a prime number.

Is there a pattern to prime numbers?

No, there is not even a single pattern in prime numbers. Simply, the set of prime numbers just acts like a random sub-sequence of the integer sequence, but obviously, it does have some pattern that we cannot describe.

What is the smallest 4 digit prime number?

Eleven is said to be as the smallest four-digit prime number in an integer base. Also, you can try an online prime factoring calculator to find the prime number before 11.

Is 2 not a prime number?

Proof: 2 is a Prime Number just enter the 2 into the designated field to check whether it is a prime number or not. Also, you can try prime number calculator to know about whether the given number is prime or not!

What is the point of prime numbers?

Prime numbers are crucial to number theorists as they’re building blocks of whole numbers, and immensely important for the world as their odd mathematical properties make them perfect for the current uses.

What is the sum of all prime numbers?

Experts answered that there are an infinite number of prime numbers, and all of which are positive integers, so that’s why the sum of all the prime numbers is infinity.

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