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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.
 
Problem 1: Find the prime factorization of 30?
Problem 2: Find the prime factorization of 147?
Problem 3: Find the prime factorization of 90?
Problem 4: Find the prime factorization of 330?
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