The number of integers which are not divisible by 3 or 7 from 1 to 10000 (including both)
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Answer:
How many numbers are there from 1 to 1000 which are not divisible by the digits 7, 3 and 5?
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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.