Question

Find the smallest and largest *composite numbers* (<n) that are relatively prime to n, where
n equals:
i. 42
ii. 60
iii. 420​

Answer 1

Given :   Numbers   42   , ii. 60     & iii. 420​

To find :  smallest and largest *composite numbers* (<n) that are relatively prime to n

Step-by-step explanation:

relatively prime to n => co prime

42 = 2 * 3 * 7

so  2 , 3 & 7 can not be factor

4 , 6 , 8  , 9 , 10 , 12 , 14 , 15 , 16 , 18 , 20 , 21 , 22 , 24 , has factor 2 , 3 or 7

25 is 5 * 5  - Smallest Composite number co prime with 42

26 , 27 , 28 , 30 , 32 , 33 , 34 , 35 , 36 , 38 , 39 , 40  has factor 2 , 3 or 7

5 * 11 = 55 > 42

Hence 25 is smallest as well largest composite which is co prime to 42

60 = 2 * 2 * 3 * 5

4 , 6 , 8  , 9 , 10 , 12 , 14 , 15 , 16 , 18 , 20 , 21 , 22 , 24 , 25 , 26 , 27 , 28 , 30 , 32 ,  33 , 34 , 35 , 36 , 38 , 39 , 40 , 42 , 44 , 45 , 46 , 48 has factor 2 , 3 or 5

49 = 7 * 7 is Smallest Composite number co prime with 60

50 , 51 , 52 , 54 , 55 , 56 , 57 , 58  has factor 2 , 3 or 5

7 * 11 = 77 > 60

Hence 49 is smallest as well largest composite which is co prime to 60

420  = 2 * 2 * 3 * 5 * 7

11 * 11  = 121   would be Smallest Composite number co prime with 420

11 * 37  =  407

13 * 31 =   403

17 * 23  = 391

19 * 19 = 361

407 is Largest Composite number that is  co prime with 420

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