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What is Prime Factorization

"Prime factorization" or "complete factorization" of the given number is nothing but the number expressed as a product of its prime factors.

Factors are the numbers that are multiplied to get another number.

3 x 5 = 15 (3, 5 are factors)

Prime factorization is a process by which a given natural number can be expressed as a product of prime numbers which are factors of the number.

A prime number is considered to be a counting number that has only two factors, the number itself and 1.

Prime Factorization Chart

The following Prime factorization chart explains us the prime factors better.

The prime factorization of a number can be found by making a factor tree.

Steps for finding prime factors:

Step 1: Find a pair of factors for a number

Step 2: Find pair of factors for the factors till all the factors are prime numbers.

What is a Prime Factor?

While factoring a number if the factored numbers are prime numbers, then the numbers are called as prime factors. In other words, "A factor which is a prime number is called a prime factor". All numbers can be expressed as a product of prime numbers. A Prime number does not have any factors apart from the number itself and 1, but 1 is not a prime number.

Example: The prime factors of 15 will be 3 and 5 (3 x 5 = 15, and 3 and 5 are prime numbers). The first 11 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31.

A factor which is a prime number is called prime factor. All number can be expressed as a product of prime numbers.

Prime Factorization Examples

The following Examples on prime factorization explains us how to find the prime factorization of a given number, This section also explain us how to draw a prime factorization tree.

1) Prime factors of 36:

Prime factorization of 36 is as follows:

The first pair of factors for 36 is 4 and 9

The prime factors of 4 are 2 and 2

The prime factors of 9 are 3 and 3

Therefore, the prime factors for 36 are 2, 2, 3 and 3

2) Prime factors of 75:

Prime factorization of 75 is as follows:

The first pair of factors for 75 is 15 and 5

The prime factors of 15 are 5 and 3

Therefore, the prime factors for 75 are 5, 5 and 3

3) Prime factors of 72:

Prime factorization of 72 is as follows:

The first pair of factors for 72 is 8 and 9

The prime factors for 8 are 2, 2 and 2

The prime factors for 9 are 3 and 3

Therefore, prime factors for 72 are 2, 2, 2, 3, and 3

4) Prime factors of 18:

Prime factorization of 18 is as follows:

The first pair of factors for 18 is 9 and 2

The prime factors for 9 are 3 and 3

Therefore, prime factors for 18 are 2, 3 and 3

5) Prime factor of 100:

Prime factorization of 100 is as follows:

The first pair of factors for 100 are 25 and 4

The prime factors for 25 are 5 and 5

The prime factors for 4 are 2 and 2

Therefore, prime factors for 100 are 5, 5, 2 and 2

6) Prime factors of 125:

Prime factorization of 125 is as follows:

The first pair of factors for 125 is 5 and 25

The prime factors for 25 are 5 and 5

Therefore, prime factors for 125 are 5, 5 and 5

Now you practice.