Question

what is the prime factorization of 135?
3 × 3 × 3 × 5 3 × 3 × 5 × 9
3 × 3 × 5 3 × 3 × 3 × 3 × 5

Explanation:

Step1: Recall prime factorization

Prime factorization means expressing a number as a product of prime numbers. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

Step2: Factorize 135

Start by dividing 135 by the smallest prime number, which is 2. But 135 is odd, so it's not divisible by 2. Next, try 3. \(135\div3 = 45\).

Step3: Continue factorizing 45

Now factorize 45. \(45\div3 = 15\).

Step4: Continue factorizing 15

Factorize 15. \(15\div3 = 5\).

Step5: Factorize 5

5 is a prime number, so we stop here.
So, combining the factors, we have \(135 = 3\times3\times3\times5\). Also, we need to check the options: 9 is not a prime number (since \(9 = 3\times3\)), so the option with 9 is incorrect. The other options either have too few or too many 3s except \(3\times3\times3\times5\).

Answer:

\(3\times3\times3\times5\) (the first option: \(3\times3\times3\times5\))