Question

1. mr. gonzales showed students part of the prime factorization of 90. one factor is missing.

$2\cdot3^2\cdot\\_\\_$
what number completes this prime factorization?

Explanation:

Step1: Recall prime factorization of 90

Prime factorization means expressing a number as a product of prime numbers. We know that \(90 = 2\times3\times3\times5\).

Step2: Analyze the given factors

The given part of the prime factorization is \(2\cdot3^{2}\cdot\underline{\quad}\). Since \(3^{2}=3\times3\), the given factors are \(2\times3\times3\).

Step3: Find the missing prime factor

To get 90, we divide 90 by the product of the given factors. First, calculate the product of the given factors: \(2\times3^{2}=2\times9 = 18\). Then, divide 90 by 18: \(\frac{90}{18}=5\). And 5 is a prime number.

Answer:

5