What are Prime Factors and Prime Factorization of a number

 Prime Number is a number that can be completely divided only by itself and one.

EXAMPE: Express 990 as a product of its prime factors.

METHOD 1:

STEP 1: Start dividing the given number by prime numbers 2, 3, 5, 7, …. one-by-one and find the smallest prime number which divides the given number completely leaving no remainder.

Here, 990 ÷ 2 = 495      (No remainder)

Now write it like this:

 

STEP 2:  Again, find the smallest prime number which divides the quotient completely leaving no remainder.

Here quotient is 495

495 ÷ 5 = 99    (No remainder)

 

STEP 3: Continue in the same way until you get 1 at the end.

The numbers in the left column are prime factors of given number.

 

So, prime factors of 990 are:

2, 5, 3, 3, 11

 

METHOD 2 (Factor Tree):

STEP 1: Find any two numbers whose product is a given number. In other words, find two factors of a given number.

990 = 99 × 10

STEP 3: Keep finding the factors until you get all prime numbers at the bottom

so, 

990 = 2 × 3 × 3 × 5 × 11

Remember: The fundamental theorem of arithmetic says that every positive integer has a unique prime factorization.

RELATED POST: