Question

Which expressions show the prime factorization of 90? Check all that apply.

A. 2 x 3 x 15
B. 2² x 3 x 5
C. 2 x 3² x 5
D. 2 x 5 x 9
E. 2 x 3 x 3 x 5

Answer 1

The correct expressions showing the prime factorization of 90 are C (2 x 3² x 5) and E (2 x 3 x 3 x 5), as they break down 90 into its prime factors correctly.

Step-by-step explanation:

The expressions that show the prime factorization of 90 are those where all numbers are prime and their product equals 90. Let's examine each option given:

• A. 2 x 3 x 15: This expression is not fully factorized since 15 is not a prime number; 15 can be further factorized into 3 x 5.
• B. 2² x 3 x 5: This expression is not correct since 2² (which is 4) should not be a factor of 90.
• C. 2 x 3² x 5: This is a correct expression of the prime factorization of 90. When calculated, 2 x 3² x 5 equals 2 x 9 x 5, which is 90.
• D. 2 x 5 x 9: This expression is similar to A as 9 is not a prime number; 9 could be further factorized into 3 x 3.
• E. 2 x 3 x 3 x 5: This expression fully breaks down 90 into prime factors. This is another correct expression of the prime factorization of 90, equivalent to 2 x 3² x 5.

Therefore, the expressions showing the correct prime factorization of 90 are C (2 x 3² x 5) and E (2 x 3 x 3 x 5).