what is the prime factorization of 132

To find the prime factorization of 132, we need to determine the prime numbers that divide evenly into it.

1. Divide 132 by the smallest possible prime number, which is 2.
132 ÷ 2 = 66

2. The result, 66, is still an even number, so we continue dividing by 2.
66 ÷ 2 = 33

3. Now, we try dividing 33 by the next prime number, which is 3.
33 ÷ 3 = 11

Since 11 is a prime number, we stop here.

Therefore, the prime factorization of 132 is: 2 × 2 × 3 × 11, or in exponent form: 2^2 × 3^1 × 11^1.

To find the prime factorization of a number, you need to determine the prime numbers that can be multiplied together to get the original number. Here's how you can find the prime factorization of 132:

First, you can start dividing the number by the smallest prime number, 2. Divide 132 by 2, and you get 66. Since 66 is also divisible by 2, divide it again by 2, giving you 33.

Now, 33 is not divisible by 2 anymore, so you move on to the next prime number, 3. Divide 33 by 3, and you get 11. At this point, you have reached a prime number.

Therefore, the prime factorization of 132 is 2 * 2 * 3 * 11, or 2^2 * 3 * 11.

In summary, you divide the original number by the smallest prime numbers until you reach a prime number, and then you do the same for the resulting quotient until all factors are prime numbers.

132/2=66

66/2=33
33/3=11

so 132=3*11*2^2

First divide by 2 and see that's left.

132 = 2 x 66
66 is 11 x 6, so let's write it as
132 = 2x11x6
Now prime-factor the 6, and you are done