Hi Student!
Prime factorization is the process of stripping down a number to it's basic elements. We take a number and bring it down the most we can. For example we take 4 and make it 2 x 2. In this case we are given a number of 252 so we can began by dividing by 2.
Looking at the numbers that we have now, 126 x 2, we can see that 126 can still be divisible by another 2 so lets do that again.
Now, looking at the numbers that we have, 63 x 2 x 2, we see that we can no longer divide it by a 2 because 63 is not divisible by 2. However, we can divide 3 away from the number so lets do that.
Once again, looking at the numbers that we have, 21 x 3 x 2 x 2, we see that we can once again divide a 3 away from our first number so lets do that again.
Finally, we have come down to the last line where our final elements are 7 x 3 x 3 x 2 x 2. This is our prime factorization of the number 252 and this is where we can conclude our solution seeking.