Question

Determine the number of multiples of 3 that are less than 1000 but not divisible by either 9 or by 1

Answer 1

Answer:

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• Step-by-step explanation:
• Being divisible (or not) by 22, 33 or 55 is a cyclic phenomenon, with a cycle length or period of 3030. Why? Because however a number behaves regarding divisibility by 22, 33 or 55, adding 3030 to it won’t change anything, since 3030 is divisible by all three of them. Adding a multiple of 33 doesn’t alter divisibility by 33. Adding a multiple of 22 or 55 doesn’t alter divisibility by 22 or 55. So adding 3030 doesn’t alter any of those.
• Therefore, the only thing we need to do is figure out how many numbers between 11 and 3030 are not divisible by 22, 33 or 55. That’s much easier than surveying the numbers between 11 and 10001000.
• Finding those numbers can be done by hand, or by the same inclusion-exclusion principle mentioned in other answers (but much easier!), or by knowing about the Euler ϕϕ function. This function counts the number of numbers between 11 and nn which

Answer 2

Answer:

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Step-by-step explanation:

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