The prime factorization of a number involves breaking it down into its prime number components. To find the prime factorization of 90, we can follow these steps:
- Start by dividing by the smallest prime: The smallest prime number is 2. Since 90 is even, we start by dividing it by 2.
- 90 ÷ 2 = 45.
- Continue with the result: Now we look at 45. The next smallest prime number is 3. We divide 45 by 3.
- 45 ÷ 3 = 15.
- Repeat the process: Now we take 15 and divide it by 3 again, since it is still divisible by 3.
- 15 ÷ 3 = 5.
- Finish with the last number: Now we have 5, which is a prime number itself. We stop here.
Putting it all together, the prime factorization of 90 can be expressed as:
2 × 3 × 3 × 5 or in exponential form as 2 × 3² × 5.
So, to summarize, the prime factorization of 90 is 2 × 3² × 5.