Converting the composite numbers in to multiplication of numbers is known as factorization, simplifying till the prime numbers is known as prime factorization.
Prime Number
A whole number greater than 1 that cannot be divided by any other number except the number and the same number is known as the prime number.
Some of the prime numbers are : 2, 3, 5, 7, 11, 13, and 17 ...
Composite numbers:
It is an integer that has more than one prime factor. They can be expressed as unique set of prime numbers. The first composite number is 4. Besides 1 each other natural number is either prime or composite number.
Prime Factorization of Composite Numbers
Prime Factorization is the method of splitting the composite number into prime numbers
Factors:
The factor is the numbers that are multiplied to get another number.
5 x 3 = 15
(5, 3 factor)
while factoring if we get the factored numbers as the prime number, then the numbers are called as prime factors.
Example: The prime factors of 15 will be 5 and 3 ( 5 x 3 =15, and 5 and 3 are prime numbers).
Examples of Prime Factorization of Composite Numbers:
Example1.
What are the prime factorization of 225?
Solution:
Here 225 is a composite number, we are going to convert into a equivalent prime number.
It is best to start with the smallest prime number that can divide the number, which is 3, so let's check:
225 ÷ 3 = 75
since 75 is not a prime number we have to factor 75
75 ÷ 3 = 25
since 25 is not a prime number we have to factor 25.
25 ÷ 5 = 5
here, 5 is a prime number, so we can stop with this
225 = 3 x 3 x 5 x 5
The prime factorization of 225 is 3 x 3 x 5 x 5
Example 2.
What are the prime factorization of 490?
Solution:
Here 490 is a composite number, we are going to convert into a equivalent prime number.
It is best to start with the smallest prime number that can divide the number, which is 5, so let's check:
490 ÷ 5 = 98
since 98 is not a prime number we have to factor 98
98 ÷ 2 = 49
since 49 is not a prime number we have to factor 49.
49 ÷ 7 = 7
here, 5 is a prime number, so we can stop with this
490 = 5 x 2 x 7 x 7
The prime factorization of 490 is 5 x 2 x 7 x 7
