15 and its multiples
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Yes; all numbers that are divisible by 9 are divisible by 3.
All numbers divisible by 3 are NOT divisible by 9. As an example, 6, which is divisible by 3, is not divisible by 9. However, all numbers divisible by 9 are also divisible by 3 because 9 is divisible by 3.
All numbers divisible by 9 are divisible by 3; since 9 = 3 x 3 all multiples of 9 are also multiples of 3. However, all numbers divisible by 3 are not divisible by 9, eg 6 = 2 x 3 but 6 is not divisible by 9 (since 6 is not a multiple of 9) - it only takes one counter example to disprove a theory.
Yes
There are 466 numbers between 1 and 1,000 that are divisible by three or five.