Prime factorization of a given number is expressing the given number as a product of all prime numbers.
Prime number is a number which has no other factors other than one and itself.
Examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29……..
Prime factorization is one of the basic and important ways to find the factors of a given number. Factors are
the numbers which multiplied together give another number. The product of all the prime factors for the number gives back the original number.
Example: Find the prime factorization of 6?
The number can be written as 6 = 2 * 3.
Here 2 and 3 are the prime numbers whose product givens back the original number 6.
Example:- Find the prime factorization of the number 92?
Solution: Given number is 92.
First Step: To find its prime factors.
we divide the given number with the smallest prime number.
92 ÷ 2 = 46; so, 96 = 46 * 2
Now the number 46 can be further divided by the prime number 2.
So here we have 46 ÷ 2 = 23.
The number 23 cannot be further divided by any other number.
Because 23 itself is a prime number divisible by one and itself.
So here we have 46 = 2 * 23.
Using the prime factorization 92 = 2 * 2 * 23.
Here 2, 2, 23 are the prime numbers whose product gives back the number 92.
Hence the given number 92 = 22 * 23.