aliquote.org

“The numbers 111, 222, 333, 444, 555, 666, 777, 888, and 999 are all evenly divisible by 37, leaving no remainder.” (via @pickover) Using base 10 notation, a three-digit number, say $aaa$, can be written as $100\cdots a + 10\cdot a + a = a \cdot (100 + 10 + 1) = a \cdot 111$. Clearly, 111 is a divisor of $aaa$ ($111 = 37\times 3$), but also of 222, 333, … Hence, all three-digit numbers that are multiple of 111 will fit the bill.