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How to Find Prime Factorization

Prime Numbers
Prime number is a number greater than "1" and is not divisible by any other number except 1 and itself. Prime numbers are positive whole numbers bigger than 1.

Prime Factors
Every number can be written in the form of product of prime numbers. These numbers are called prime factors of that number. Every number has a unique set of prime factors.

For example: 6 can be written as:
$6=2\times 3$, where 2 and 3 are referred as prime factors of 6.

Prime Factorization
The method of finding prime factors of a numbers is known as prime factorization. In other words, prime factorization is the technique of determining prime numbers which multiply together to give the required number.
Prime factorization method is illustrated below:
Step 1 : Find a prime number by which the given number is divisible.
Step 2: Divide the given number by that prime number and write down the result.
Step 3: Now determine a prime number by which the result obtained (in step 2) is divisible. Divide it by that number.
Step 4: Repeat this process until reach at 1.
Step 5: All the prime numbers obtained in this process will be the prime factors of given number.
Let us understand prime factorization method by an example.

Example: Evaluate prime factors of 384 using prime factorization method.
Solution: The method is illustrated in the following figure:
Prime Factorization
Hence, prime factorization of 384 is:
$384=2\times 2\times 2\times 2\times 2\times 2\times 2\times 3$

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