Question

The number of integers which are not divisible by 3 or 7 from 1 to 10000 (including both)
​

Answer 1

Answer:

How many numbers are there from 1 to 1000 which are not divisible by the digits 7, 3 and 5?

6 Answers

Profile photo for Akshay Tandon

Akshay Tandon, works at Masterpiece Coaching Classes (2016-present)

Answered 3 years ago

Number of digits divisible by 3 ——

starting from 3 to 999. Total 333.

Number of digits divisible by 5 ——

starting from 5 to 1000. Total 200.

Number of digits divisible by 7——-

starting from 7 to 1000. Total 142.

Number of digits divisible by 3 and 5 together--- starting from 15 to 1000. Total 66.

Number of digits divisible by 3 and 7 together—- starting from 21 to 1000. Total 47.

Number of digits divisible by 5 and 7 together—- starting from 35 to 1000. Total 28.

Number of digits divisible by 3, 5 and 7 altogether—- starting from 105 to 1000. Total 9.

Now total digits divisible by 3, 5, 7 are

675–47–28–66+9=543.

So numbers which are not divisible by 3,5 and 7 are 1000–543=457.