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There are 250 three-digit numbers that divide by 4.

To calculate this, we can use the formula for the number of integers between two numbers (a and b): (b - a) + 1.

In this case, a is 100 (the smallest three-digit number) and b is 999 (the largest three-digit number).

We can then plug these values into the formula to get: (999 - 100) + 1 = 900.

However, not all 900 three-digit numbers divide by 4. To find out how many do, we need to find out how many of the 900 numbers are divisible by 4.

We know that all numbers divisible by 4 end in either 0, 4, 8, or 2. This means that there are 225 numbers that end in 0, 225 numbers that end in 4, 225 numbers that end in 8, and 225 numbers that end in 2.

Therefore, there are a total of 900 numbers that are divisible by 4.

Finally, we can calculate the total number of three-digit numbers that divide by 4 by subtracting the number of three-digit numbers that are not divisible by 4 (675) from the total number of three-digit numbers (900).

This gives us: 900 - 675 = 250 three-digit numbers that divide by 4.