What is the largest 4-digit number that can be evenly divided by every single digit integer?

1*5*7*8*9=2520 which is the smallest 4 digit number satisfying the requirements.

2520*3=7560 , the largest number satisfying the requirements.

This is a trick question. Zero is a single digit integer, and since you cannot divide by zero there is no 4 digit number satisfying this constraint.

From https://en.wikipedia.org/wiki/Division_by_zero:

"In mathematics, a division is called a division by zero if the divisor is zero. Such a division can be formally expressed as a / 0 where a is the dividend. Whether this expression can be assigned a well-defined value depends upon the mathematical setting. In ordinary (real number) arithmetic, the expression has no meaning."

It's worth noting that Bronxiteone's answer is correct if you say "every POSITIVE single digit integer".

I would additionally qualify that 2520 is the smallest number (4 digit or not) satisfying that requirement. To understand where 1*5*7*8*9 came from, list the numbers from 1 - 9 by their prime factorizations:

1 * 2 * 3 * (2^2) * 5 * (2*3) * 7 * (2^3) * (3^2)

Pick the least number of factors needed to express every number:

Using 3^2 gets 9 & 3
Using 2^3 gets 2, 4, & 8, and using a 3 from 3^2 gets us 8
Using 5 & 7 gets us 5 & 7
Using 1 gets us 1

That's all of them, and it multiplies out to 2520. To find the largest 4 digit number that can be evenly divided by every POSITIVE single digit integer is the same as finding the largest multiple of 2520 that is 4 digits. This is done by multiplying it by 3 to get 7560.

Thanks all. THe answer by Bronxiteone was what I was looking for, but Juggernaut314 was correct by pointing out the flaw of my stated question.
Thanks to you both.

Eleven is the smallest number NOT divisible by any one digit positive number except one.