What is the greatest odd factor of the number 2,112?

To find the greatest odd factor of 2,112, it’s important to first analyze the number by determining its prime factorization.

The number 2,112 can be broken down into its prime factors. It is an even number, which indicates that its prime factorization will contain the factor of 2. When fully factored, 2,112 breaks down into:

[ 2,112 = 2^4 \times 3 \times 11 ]

From this factorization, we note that the odd component is derived from the multiplication of the 3 and the 11, since odd numbers are not affected by factors of 2. To find the greatest odd factor, we multiply all odd prime factors together:

[ 3 \times 11 = 33 ]

Thus, 33 is the largest odd factor arising from the prime factorization of 2,112.

Examining the other options, it becomes clear they do not meet the criteria for being the greatest odd factor derived from the breakdown of 2,112. Therefore, 33 is indeed the correct answer, as it is the highest number that can be produced solely from the odd prime factors within the factors of 2,112.