Prime Factorization Methods
Two common methods of Prime Factorization are:
- Division Method
- Factor Tree Method
Prime Factorization by Division Method
In this method, the number is successively divided by prime numbers until the quotient becomes 1, with each division identifying a prime factor.
Steps to identify the prime factors of a number by Division Method :
Step 1: Divide the number by the smallest prime number (i.e. 2) until we are able to divide the given number without leaving any remainder.
Step 2: Move on to the next prime number and repeat the division until the quotient becomes 1.
Step 3: The prime factors are the divisors used in the division process.
Let’s consider some examples for better understanding.
Example 1: Find the Prime Factorization of 60 using Division Method.
Prime factorization of 60 using the division method can be given as follows:
Prime Factorization by Division Method
Example 2: Find the Prime Factorization of 210 using Division Method.
Prime factorization of 210 using the division method can be given as follows:
Prime Factorization by Division Method
Example 3: Express 56 as the product of its Prime Factors.
To express 56 as the product of its prime factors, we need to find the prime factors of 56 first. Prime factorization of 56 can be evaluated as follows:
Prime Factorization by Division Method
Prime Factorization by Factor Tree Method
The Factor Tree Method involves breaking down a number into its prime factors by constructing a tree-like structure called a factor tree.
Steps to identify the prime factors of a number by Factor Tree Method:
Step 1: Identify two factors of the number that are not prime.
Step 2: Write these two factors as branches of the factor tree.
Step 3: Repeat steps 1 and 2 for each non-prime factor until all branches end with prime numbers.
Step 4: The prime factors are the numbers at the end of the branches.
Let’s consider some examples for better understanding as follows:
Example 1: Find the factorization of 60 by the Factor Tree Method.
Solution:
Factor tree of 60 is given as follows:
Example 2: Make the Factor Tree of 210.
Solution:
Factor tree of 210 is given as follows:
Prime Factorization of 210 by Factor Tree
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Prime Factorization
Prime Factorization is a way of writing numbers as the product of prime numbers. Prime numbers are natural numbers that have only two divisors, 1 and themselves. Composite numbers, on the other hand, have more than two divisors.
Let’s learn how to perform the prime factorization of numbers step by step.
Table of Content
- Prime Factorization Definition
- Prime Factors
- Prime Factorization of Numbers
- Prime Factorization Methods
- Prime Factorization Examples