Question

How many numbers between 1 and 1000 are not divisible by 3 5 or 7?

Answer 1

Number of digits divisible by 3 —— starting from 3 to 999. Total 333.

Number of digits divisible by 5 —— starting from 5 to 995. Total 199.


Number of digits divisible by 7——- starting from 7 to 994. Total 142.

Number of digits divisible by 3 and 5 together--- starting from 15 to 990. Total 66.

Number of digits divisible by 3 and 7 together—- starting from 21 to 987. Total 47

.Number of digits divisible by 5 and 7 together—- starting from 35 to 980. Total 28.

Number of digits divisible by 3, 5 and 7 altogether—- starting from 105 to 945. Total 9.

So the count of numbers which are divisible by either 3,5 or 7 from 1 to 1000 will be : (333+199+142–66–47–28+9) i.e, 542

So the count of numbers that are not divisible will be (1000–542) which is 458

Hence the answer. :)