Find Prime Factorization of 180 Express in Exponential Form

To find the prime factorization of 180 and express it in exponential form, we need to break down the number into its prime factors. Here’s a step-by-step solution:

Step 1: Divide by the smallest prime number

The smallest prime number is 2. We start by dividing 180 by 2.

180 ÷ 2 = 90

So, we have one factor: 2.

Step 2: Continue dividing by 2

Next, we take the result (90) and divide it by 2 again.

90 ÷ 2 = 45

Now we have two factors of 2: 2 × 2.

Step 3: Move to the next prime number

The next smallest prime number is 3. Now we divide 45 by 3.

45 ÷ 3 = 15

This gives us a factor of 3: 3.

Step 4: Continue dividing by 3

Next, we take 15 and divide it by 3 again.

15 ÷ 3 = 5

Now we have two factors of 3: 3 × 3.

Step 5: Factor the remaining number

We are left with 5, which is a prime number itself. So, we have another factor: 5.

Step 6: Combine all factors

Now we combine all the prime factors we found:

180 = 2 × 2 × 3 × 3 × 5

In exponential form, we can express this as:

22 × 32 × 51

So, the prime factorization of 180 expressed in exponential form is:

22 × 32 × 5