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We know that

12 = 3 x 4
 

But, can we write 12 as the product of just prime numbers?

Well, 3 is a prime number, but 4 isn't.

Can we break 4 into a product of primes?

4 = 2 x 2
 

So,12 = 3 x 2 x 2

 

When we write a number as the product of primes, it's called a prime factorization.

Smaller numbers are pretty easy to do...  You just start with your times tables numbers ( like I did with 12 ):

Find the prime factorization of 18:

From our times tables

18 = 3 x 6
 

3 is prime, but we need to break the 6 up!

18 = 3 x 2 x 3
 

It's polite to put the factors in order from least to greatest:

18 = 2 x 3 x 3
 

Here it is with exponents:

18 = 2 x 3^2