Prime Factorization Of Composite Numbers

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