What is Prime Factorization | Prime Factorization 2 Easy Methods

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What is Prime Factorization

“Prime Factorization” is the process of determining which prime numbers multiply together to form the original number. Prime numbers are numbers that have only two factors, 1 and the number itself. For example 2, 3, 4, 5, and so on.


What are the Prime Factors of 14?

It is best, to begin with, the smallest prime number, which is 2, so let’s see:

12 ÷ 2 = 6

Yes, it is divided by two exactly. We’ve already taken the first step!

However, 6 is not a prime number, so we must proceed. Let’s try number two again:

6 ÷ 2 = 3

Yes, that also worked. And because 3 is a prime number, we have the answer:

12 = 2 × 2 × 3

Because every factor is a prime number, the answer is correct.

Methods of Prime Factorization

There are several methods for prime factorization. The following are the most common :

1. Factor tree method: The factor tree method finds a number’s factors, which are then factorized further until we reach the prime numbers. With the help of the following example, we will learn how to prime factorize a number using the factor tree method.

Prime Factorization | Factor Tree of 72

2. Division Method: The division method can also be used to find the prime factors of a large number by dividing it by prime numbers. Let’s look at an example to see how we can use the division method to find the prime factors of a number.

Video Explanation


Q.1. What is prime factorization?

Ans. Prime numbers have two factors: 1 and the number itself. For instance, 2, 3, 5, 7, 11, 13, 17,…, and factorization is the process of writing the number or expression as the product of its factors. Thus, prime factorization is the process of factorizing a given number as the product of its prime factors.

Q.2. What is the prime factorization of 75?

Ans. Because 75 has more than two positive factors, it is not a prime number.
75= 1×75
75= 5×15
= 5x 5×3
75= 3×25
= 3x5x5
so, 75= 3x 5²

Other Maths Concepts

To understand other maths concepts, please check our other articles:

  1. Rational and Irrational Numbers
  2. What are Natural Numbers
  3. Integers Definition With Easy Examples | What Are Integers
  4. Whole Numbers | Definition, Examples, Full Explanation
  5. Imaginary Numbers Definition With Easy Examples
  6. Real Numbers Definition | Real Numbers Examples
  7. Simple Explanation of Composite Numbers

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