What is Prime Factorization?

by Rohan Mathew
What is Prime Factorization

What are Prime Numbers?

A natural number that has a value greater than one but cannot be expressed as a product of two or more numbers is called a prime number. On the other hand, a composite number is any natural number that is greater than 1 but is not a prime number. Such numbers can be expressed as a product of two or more numbers. Prime numbers are used in prime factorization. According to the Fundamental Theorem of Arithmetic, all the natural numbers that are greater than 1 can be categorized as either a prime number or can be expressed as a product of primes. This product is unique to every composite number.

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What is Prime Factorization?

The process of decomposing a composite number into a product of smaller integers is known as integer factorization. If these factors are only restricted to prime numbers, then such a process is known as prime factorization. Thus, if we want to find the prime factors of a composite number, we will apply the prime factorization method. Suppose we are required to find the prime factors of a number. The first step that needs to be done is dividing the number by the least possible prime number that will leave no remainder. The quotient that is produced needs to be again divided by the least prime number, and we continue to repeat these steps till the quotient that is produced is not 1. Let us look at a simple example to get a better idea of how to apply the concept of prime factorization.

Example: List out the prime factors of 50 using the prime factorization method. 

Step 1: Divide 50 by the smallest prime factor. 

As 2 is the smallest prime that can completely divide 50 without a remainder, that becomes our first prime factor. 50 / 2 = 25.

We are now left with the quotient 25.

Step 2: Divide 25 with the smallest prime number

As 5 is the smallest prime that can divide 25, that becomes our next prime factor. 25 / 5 = 5. Now our quotient is 5.

Step 3: Divide 5 by the smallest prime

5 is completely divisible by itself, and it also forms the smallest prime number that can divide it; we get 5 / 5 = 1. Thus, our quotient is 1, and we have successfully factorized 50.

Prime Factorization of 50 = 2 * 5 * 5

Another point to note is that no other number can have the same prime product sequence as 50. 

Uses of Prime Factorization

Prime Factorization is vastly used in Mathematical topics to help speed up calculations. For example, the most efficient method to calculate the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of numbers is prime factorization. It also helps with finding square roots of a given number. 

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Conclusion

One of the earliest fields of Mathematical research was prime numbers, as they form a vital part of number theory. Learning about prime factorization can help kids increase their speed and accuracy in solving sums and also improve their mental arithmetic power. Hence, it is vital for young minds to have an in-depth knowledge of this concept. The best way to learn about primes and how to use them is by approaching a good coaching institute such as Cuemath. Cuemath provides an outstanding quality of education to children and focuses on building a robust foundation in Math. The certified tutors allow kids to maintain their flexibility so that they do not get pressured while studying. The goal is always to combine fun with learning to give children an enjoyable learning experience. 

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