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Prime Factorization By Division Method

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Last updated date: 09th Apr 2024
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Introduction

Prime factorization is a method to find the prime factors of the given number with the help of different composite numbers. We know that a composite number has more than two factors; so this method is applicable for all the composite numbers.


For example:

5 is a prime number which has two factors  5×1, whereas a composite number has more than two factors present in it. For example 15 has three factors such as 1×3×5.


Prime Factorization by Division Method

We know that there are two different methods of prime factorization:


  • Division Method 

  • Factor Tree Method 


We can hear discussion about the division method. In this method we will divide the large number to the small prime numbers to find the factors. In other words we can say that the division method is used to find out the prime factors of a large number by dividing the number by different prime numbers.


Division by Primes

In the prime factorization method we have to divide the large number with the small prime numbers. This method is known as the division method. For example 60 is a composite number and we have to find its prime factors. So we have different methods but we have to divide with the prime number,

60 = 2×2×3×5


Prime Factorization Steps

These are the steps of prime factorization

  • Divide the given number by the smallest prime numbers ( in this case we have to find the smallest prime number which can divide the number exactly).

  • Again divide the quotient by the smallest prime number (it can be the same or a different prime number).

  • Repeat the procedure until the quotient becomes 1.

  • At the end multiply all the prime factors. ( One thing we have to remember is that the product is the number itself).


Prime Factors of 16

First of all 16 is a composite number and we have to find its prime factors;


  • As we consider it to be the smallest prime number.

  • We get 8 and again by 2

  • Then we get 4 again we dividing by 2

  • Then we get 2 again dividing by the smallest prime number 2.

  • We get a quotient as 1.

16=2×2×2×2


Prime Factorization of 16


Prime Factorization of 16


How to Get Prime Factorization

We can get prime factorization by using the both methods; 1) factor tree method, 2) division method. These methods help us to get the prime factorization.

For example:


Factor Tree Method and Continuous Method


Factor Tree Method and Continuous Method


Solved Examples

1. What is the prime factorization of 90.

Solution:

Step 1: divided by the smallest prime number 2

 90÷2 = 45

Step 2: divided by 3

45÷3 = 15

Step 3: divided by 3

15÷3 = 5

Step 4: divided by 5

5÷5 = 1

Ans. 2×3×3×5= 90


Solved Questions

1. Find the prime factors of 40.


Solution 


Prime Factorization of 40.


Prime Factorization of 40.


Ans. 2×2×2×5 = 40


2. Find prime factorization of 24.


Solution: 


Prime Factorization of 24


Prime Factorization of 24


Ans. 24=2×2×2×3


Summary

In this article we learn about the different types of prime factorization, mainly we learn about the division method by prime factorization and its rules or steps. The most important uses of prime factorization are cryptography, HCF and LCM. Prime factorization is really helpful for us.

FAQs on Prime Factorization By Division Method

1. What is prime factorization?

Prime factorization of any number means to define the number as the product of different small prime numbers.

For example; the prime factorization of 20 is

2×2×5

Here to add 5 are the prime factors of 20.

2. What are the types of prime factorization?

There are two types of prime factorization

  1. Factor Tree Method

  2. Division Method

3. What are prime numbers?

A prime number is a natural number which is greater than 1 and it can be divided by one or itself.

4. What is a composite number?

A natural number which is greater than 1 and not a prime number is called a composite number.

5. What are prime factors?

Any prime number that can be multiplied with others to give the original number is called prime factors.