If N is the set of natural numbers that are factors of 16, choose the selection below that correctly shows this set in roster form.
(1 point)
{1, 2, 4, 8, 16}
(2, 4, 6, 8, 10, 12, 14, 16}
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
{2, 4, 8}
The correct selection that shows the set N in roster form is:
{1, 2, 4, 8, 16}
The correct selection that shows the set of natural numbers that are factors of 16 in roster form is:
{1, 2, 4, 8, 16}
To find the set of natural numbers that are factors of 16, we need to divide 16 by all possible natural numbers and check if the division results in a whole number (no remainder). The factors of 16 are the numbers that divide 16 without leaving a remainder.
Let's go through the options:
Option 1: {1, 2, 4, 8, 16}
To check if these numbers are factors of 16, we divide 16 by each of them:
16 ÷ 1 = 16 (no remainder)
16 ÷ 2 = 8 (no remainder)
16 ÷ 4 = 4 (no remainder)
16 ÷ 8 = 2 (no remainder)
16 ÷ 16 = 1 (no remainder)
Option 2: {2, 4, 6, 8, 10, 12, 14, 16}
This option contains numbers that are not factors of 16. For example, when we divide 16 by 6, we get 16 ÷ 6 = 2 remainder 4, which means 6 is not a factor of 16.
Option 3: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
This option contains all the natural numbers from 1 to 16. While some of these numbers are indeed factors of 16, there are also numbers that are not factors of 16, such as 3, 5, 6, 7, 9, etc.
Option 4: {2, 4, 8}
To check if these numbers are factors of 16, we divide 16 by each of them:
16 ÷ 2 = 8 (no remainder)
16 ÷ 4 = 4 (no remainder)
16 ÷ 8 = 2 (no remainder)
Therefore, the correct set of natural numbers that are factors of 16 in roster form is: {1, 2, 4, 8, 16}. Hence, the correct answer is option 1.