Answer:
The number of integers greater than 10 and less than 30 which are relative prime with 28 is: nine (9).
Step-by-step explanation:
Two numbers are said to be relative prime if their greatest common factor is 1.
Integer greater than 10 and less than 30 are:
11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29
Let list all the factors of each number and compare individually with 28 to determine if it is relative prime with 28.
11 = 1, 11
12 = 1, 2, 3, 4, 6, 12
13 = 1, 13
14 = 1, 2, 7, 14
15 = 1, 3, 5, 15
16 = 1, 2, 4, 8, 16
17 = 1, 17
18 = 1, 2, 3, 6, 9, 18
19 = 1, 19
20 = 1, 2, 4, 5, 10, 20
21 = 1, 3, 7, 21
22 = 1, 2, 11, 22
23 = 1, 23
24 = 1, 2, 3, 4, 6, 8, 12, 24
25 = 1, 5, 25
26 = 1, 2, 13, 26
27 = 1, 3, 9, 27
28 = 1, 2, 4, 7, 14, 28
29 = 1, 29
Let remove all the numbers that have a factor common with 28 other than 1 because we only want 1 to be the common factor. We are left with the following list:
11, 13, 15, 17, 19, 23, 25, 27, 29.
If we check the greater common factor (GCF) for each of the above number relative to 28, we get 1.
- GCF{11, 28} = 1
- GCF{13, 28} = 1
- GCF{15, 28} = 1
- GCF{17, 28} = 1
- GCF{19, 28} = 1
- GCF{23, 28} = 1
- GCF{25, 28} = 1
- GCF{27, 28} = 1
- GCF{28, 29} = 1
