Question

1. what is the greatest common factor that could be used to reduce 36/90? a. 18 b. 6 c. 9 d. 14

Explanation:

Step1: Find factors of 36

The factors of 36 are \(1, 2, 3, 4, 6, 9, 12, 18, 36\).

Step2: Find factors of 90

The factors of 90 are \(1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90\).

Step3: Identify common factors

Common factors of 36 and 90 are \(1, 2, 3, 6, 9, 18\).

Step4: Determine the greatest common factor (GCF)

Among these common factors, the greatest one is 18? Wait, no, wait. Wait, let's check again. Wait, 36 ÷ 18 = 2, 90 ÷ 18 = 5. But wait, the options: A is 18, B is 6, C is 9, D is 14. Wait, but let's check the GCF. Wait, prime factorization of 36: \(2^2\times3^2\), prime factorization of 90: \(2\times3^2\times5\). So GCF is \(2\times3^2 = 18\)? But wait, the options have 18 as option A. Wait, but let's check the division. 36 ÷ 18 = 2, 90 ÷ 18 = 5. So 36/90 = 2/5 when divided by 18. But wait, the question is "the greatest common factor that could be used to reduce 36/90". So the GCF of 36 and 90 is 18. But let's check the options. Option A is 18, which is a common factor and the greatest. Wait, but maybe I made a mistake. Wait, let's check the options again. The options are A.18, B.6, C.9, D.14. So the GCF of 36 and 90 is 18. So the answer should be A. Wait, but let's confirm. Factors of 36: 1,2,3,4,6,9,12,18,36. Factors of 90:1,2,3,5,6,9,10,15,18,30,45,90. Common factors:1,2,3,6,9,18. Greatest is 18. So the greatest common factor is 18. So the answer is A.

Answer:

A. 18