Question

The number of positive integers which are less than or equal to 1000 and are divisible by none of 17, 19 and 23 equals

Answer 1

Answer:

Step-by-step explanation:

numbers less than or equal to 1000 those are divisible by

17

17,34,.......

1000/17 = 58 + 14/17

by 19

1000/19 = 52 + 12/19

by 23

1000/23 = 43 + 11/23

total numbers are = 58 + 52 + 43 = 153

so the numbers which are not divisible by 17, 19, 23 are 1000-153 = 847

Answer 2

Answer:

Step-by-step explanation:

Numbers less than thousand divisible by 17 = 1000/17 ≡ 58

Numbers less than thousand divisible by 19 = 1000/19 ≡ 52

Numbers less than thousand divisible by 23 = 1000/23 ≡ 43

Numbers less than thousand divisible by both 17 & 19 = 1000/(17*19) ≡ 3

Numbers less than thousand divisible by both 17 & 23 = 1000/(17*23) ≡ 2

Numbers less than thousand divisible by both 23 & 19 = 1000/(23*19) ≡ 2

Total Numbers less than thousand divisible by 17, 19, 23 = 58 + 52 + 43 - 3 - 2 - 2 = 146

Total Numbers less than thousand not divisible by 17, 19, 23 = 1000 - 146 = 854