To begin, we know that 9000 will be a four-digit number that has both 25 and 30 as factors, since 9 is divisible by 3, and the number has a final two digits that are divisible by 25 (an even hundred). However, this is not the largest four-digit number. We can do the same with 9900, since 99 is a multiple of 3, as well, and is still a round-hundred. We know that 9925, 9950, and 9975 are not divisible by 30 evenly, so the largest four-digit number divisible by 25 and 30 is 9900.
