What is the prime factorization of 396?

To find the prime factorization of 396, we begin by dividing the number by the smallest prime numbers until we can no longer divide.

First, we can divide 396 by 2, which is the smallest prime number:

• 396 ÷ 2 = 198

Next, we continue by dividing 198 by 2:

• 198 ÷ 2 = 99

Now we have 99, which is not divisible by 2. So we move to the next prime number, which is 3:

• 99 ÷ 3 = 33

Then we divide 33 by 3 again:

• 33 ÷ 3 = 11

Finally, we are left with 11, which is a prime number itself.

So, the prime factorization of 396 is:

• 2 x 2 x 3 x 3 x 11
• or, expressed in exponent form: 2² x 3² x 11

This means that if you multiply 2 x 2 x 3 x 3 x 11 together, you will return to the original number, 396.