Question

Mr. Gonzales showed students part of a prime factorization of 90. One factor is missing though.

2 x 3^2 x _

A) 2

B) 5

C) 6

D) 10

Answer 1

The missing factor in the prime factorization of 90 is 5, as 2 x 3^2 x 5 equals 2 x 9 x 5, which is 18 x 5, giving us the final product of 90.

Step-by-step explanation:

The question requires us to find the missing factor in the prime factorization of the number 90. Given the partial factorization 2 x 32 x _, we need to multiply these factors to equal 90. The known factors multiply to give us 2 x 9, which is 18. So, we have a partial product of 18, and we need to determine what missing prime factor, when multiplied by 18, will give us the final product of 90.

Dividing 90 by the partial product of 18, we get 90 / 18 = 5. Thus, the missing factor is 5. This is because 2 x 32 x 5 equals 2 x 9 x 5, which is 18 x 5, equating to 90.

The correct prime factorization of the number 90 is therefore 2 x 32 x 5.