Let Dn be the set of positive integers that divide evenly into n. List the elements...

Let Dn be the set of positive integers that divide evenly into n. List the elements of each of the sets D₆, D₁₆, D₁₂, and D₃₀

Solutions

Expert Solution

Here, when it is said that "something is divided evenly into 'n' " , then 'n' becomes the dividend and that 'something' becomes divisor. i.e., We are required to find the factors of 'n' which are positive integers.

1) D6

1 divides into 6 evenly (i.e., 6/1 = 6 and 6 is integer)
2 divides into 6 evenly (i.e., 6/2 = 3 and 3 is integer)
3 divides into 6 evenly (i.e., 6/3 = 2 and 2 is integer)
6 divides into 6 evenly (i.e., 6/6 = 1 and 1 is integer)

D6 = {1,2,3,6}

2) D16

1 divides into 16 evenly (i.e., 16/1 = 16 and 16 is integer)
2 divides into 16 evenly (i.e., 16/2 = 8 and 8 is integer)
4 divides into 16 evenly (i.e., 16/4 = 4 and 4 is integer)
8 divides into 16 evenly (i.e., 16/8 = 2 and 2 is integer)
16 divides into 16 evenly (i.e., 16/16 = 1 and 1 is integer)

D16 = {1,2,4,8,16}

3) D12

1 divides into 12 evenly (i.e., 12/1 = 12 and 12 is integer)
2 divides into 12 evenly (i.e., 12/2 = 6 and 6 is integer)
3 divides into 12 evenly (i.e., 12/3 = 4 and 4 is integer)
4 divides into 12 evenly (i.e., 12/4 = 3 and 3 is integer)
6 divides into 12 evenly (i.e., 12/6 = 2 and 2 is integer)
12 divides into 12 evenly (i.e., 12/12 = 1 and 1 is integer)

D12 = {1,2,3,4,6,12}

4) D30

1 divides into 30 evenly (i.e., 30/1 = 30 and 30 is integer)
2 divides into 30 evenly (i.e., 30/2 = 15 and 15 is integer)
3 divides into 30 evenly (i.e., 30/3 = 10 and 10 is integer)
5 divides into 30 evenly (i.e., 30/5 = 6 and 6 is integer)
6 divides into 30 evenly (i.e., 30/6 = 5 and 5 is integer)
10 divides into 30 evenly (i.e., 30/10 = 3 and 3 is integer)
15 divides into 30 evenly (i.e., 30/15 = 2 and 2 is integer)
30 divides into 30 evenly (i.e., 30/30 = 1 and 1 is integer)

D30 = {1,2,3,5,6,10,15,30}

Colby Messinger answered 10 months ago

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