all numbers whose last digits are 5 and 0
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If the number ends in 5 or 0 the whole number is divisible by 5.
If a number is divisible by 5 and 7, it's divisible by 35.
A number is divisible by 15 if it is divisible by the prime factors of 15, that is, 5 and 3.
There is no easy rule for divisibility by 34.
The divisibility rule of 3 is that you add the digits together and then if the number you come up with is divisible by 3, then the number itself is divisible by 3. In this instance, 5 + 8 + 5 = 18/3 = 6, therefore, 585 is divisible by 3.