Question

how many non prime numbers between 107 and 199 both included are possible such that they are not divisible by 2 ,3, 4 ,5 ,6, 7, 8 ,9​

Answer 1

Given : non prime numbers between 107 and 199

To Find :  How many are not divisible by 2 ,3, 4 ,5 ,6, 7, 8 ,9​

Solution:

non prime numbers between 107 and 199

they are not divisible by 2 ,3, 4 ,5 ,6, 7, 8 ,9​

Hence   smallest factor is 11   as 10 can not be factor

107/11  > 9

18  < 199/11  

Hence all factors must lie between  9 and 18

9 , 10 , 12 , 14 , 15 , 16 , 18 are neglected as they are either divisible by 2 or 3

Hence Only possible factors are 11 , 13 , 17 ,

11 x 11  = 121

11 x 13 = 143

11 x 17  = 187

13 x 13  = 169

13 x 17  = 221

17 x 17 = 289

Between  107 and 199   are

121 , 143 , 169 , 187

4 non prime numbers between 107 and 199 such that they are not divisible by 2 ,3, 4 ,5 ,6, 7, 8 ,9​

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