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Prime Factorization

The positive integers that are greater than 1 and divisible only by 1 and itself are known as prime numbers. For example :-  2, 3, 5, 7, 11, 13, 17, ... etc.
In order to know about prime factorization, first we need to have knowledge of factors:
Factors: Factors of a number is a set of numbers which when multiplied together results in the given number. There can be more than one set of factors for a number.

For example: 24 has following set of factors:
24 = 24 x 1
24 = 12 x 2
24 = 4 x 6
24 = 8 x 3
24 = 2 x 2 x 2 x 3

Prime Factors: Prime factors are the factors of a number which are exclusively prime. These are the positive integers that are prime as well as factors of a given number. Prime factors are the prime numbers that exactly divide the given number.
In above example, there are many set of factors, but last one will be categorized as set of prime factors.

Prime Factorization: The process of finding prime factors of a number is known as prime factorization. In order to find prime factors by this technique, one should follow the steps given below:

  • Write the number and form a grid as we do in division.
  • Choose the smallest prime number by which given number is divisible.
  • Write the quotient down and choose another prime number by which this quotient is divisible.
  • Repeat the entire process till getting 1 at the end.
  • Multiplying all the prime factors together to get the given number again.
Let us understand this method with the help of following example:

Factorize 486 and 96 using prime factorization technique.
Prime factorization of 486 is given below:

486 = 2 x 3 x 3 x 3 x 3 x 3 = 2 x $3^{5}$

Prime factorization of 96 is given below:

96 = 2 x 2 x 2 x 2 x 2 x 3 = $2^{5}$ x 3

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