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How to Find the Prime Factorization of a Number?



Prime Factorization of a Number

Prime numbers are one of the most important concepts of mathematics, and it has numerous applications in the real world such as cryptography, card security and so on. In Mathematics, every number is made up by multiplying prime numbers. We can find out what prime numbers make an original number by using prime factorization.

Prime Factorisation is an interesting concept. It lets you find the factors of a number. In fact, each and every number is a product of its prime. The concept of prime factorization of a number is quite simple. Once students get accustomed to the concept, they enjoy solving it. In this blog, we will cover the topic of prime factorization and list out various interesting ways to find the factors of a given number.

Let’s dive in then!

Prime Factorization – Definition

The process of finding out the prime numbers which make an original number is known as prime factorization. We can find the prime factorization of a given number by various methods. Prime Factorisation is basically performed on composite numbers in order to find its prime factors. It is also used in finding the LCM  ( Least Common Multiple ) and the HCF or GCF ( Highest or Greatest Common Factor.

In this blog, we will go through some of these methods in order to get a crystal clear understanding of the concept of Prime Factorisation.

Methods to Find Prime Factorization

Division Method

In this method, we find out the prime factors of a given number by using the following steps :

  • Step – 1: We first divide the given number by the smallest prime number, which divides this number exactly. E.g. 320/2 = 160
  • Step- 2: Now, we need to divide this quotient by the smallest prime number. Following the above example, we now have 160/2 = 90
  • Step 3: We now repeat step-2 until the quotient is one. (Upon following this, we get six times the multiple of 2 and one time 5)
  • Step 4: We can now see all the prime factors in multiples. i.e. 320 = 26 x 5

Factor Tree Method

In order to find the prime factorization by factor tree method, we need to follow the following steps:

  • Step 1: The first step is imagination. You need to imagine this number as a root of a tree. Let’s assume the number is 24.
  • Step 2: Now write down any two factors of that tree. The pair of factors needs to be listed below the number which we considered as the root of that tree. The pair of composite factors for 24, in this case, is 6 and 4
  • Step 3: The listed two factors of the given number needs to factorize. Once you factorize the given number, list down the composite factors below the factors. Upon factorization of 6 and 4, we get its factors (2,3) and (2,2) respectively.
  • Step 4: Step-3 is repeated until we find the prime factors of the composite numbers in the above steps. From our example, we do not need any further factorization as per our example as we have already got the product of primes.

The factor tree method is simple and fun! You just need to find two composite factors of a number and the rest steps follow through. I hope you enjoyed learning Prime Factorisation with the help of these methods. Cuemath is an online learning platform that helps you understand these methods with the help of visual tools that can help you develop rock-solid concepts.

I hope this blog helped you understand how to find the prime factorization of a given number. Remember, regular practice of these methods can be beneficial in the long run as it gives you a speed boost and keeps you way ahead in the game! Happy Learning.

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