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.
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.
Example of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29……..
Example: Find the prime factorization of 9?
The number can be written as 9 = 3 * 3.
Here 3 and 3 are the prime numbers whose product givens back the original number 9.
Example: Find the prime factorization of the number 98?
Solution: Given number is 98.
First Step: To find its prime factors. we divide the given number with the smallest prime number.
98 ÷ 2 = 49; so, 96 = 49 * 2
Now the number 49 cannot be further divided by the prime number 2.
The next prime number 3 needs to be checked for the division.
The number 49 is not divisible by 3.
The number 49 is not divisible by the next prime number 5.
Check for the next prime number 7.
Here 49 is divisible by 7.
Using the prime factorization 98 = 2 * 7 * 7.
Here 2, 7, 7 are the prime numbers whose product gives back the number 98.
Hence the given number 98 = 72 * 2.