Sure, let's solve this math problem step-by-step:
1. Define the Range: We need to consider all the integers between 400 and 500, including both endpoints. So, our range is from 400 to 500.
2. Identify Divisibility by 3: The key objective is to identify which of these integers are divisible by 3. A number is divisible by 3 if there is no remainder left when the number is divided by 3.
3. Check Each Number in the Range: Starting from 400, we will check each number up to 500 to see if it yields zero when divided by 3.
4. List the Divisible Numbers: As we find numbers that are divisible by 3, we will list them out.
By doing this, we determine that the numbers from 400 to 500, inclusive, that are divisible by 3 are as follows:
[tex]\[ 402, 405, 408, 411, 414, 417, 420, 423, 426, 429, 432, 435, 438, 441, 444, 447, 450, 453, 456, 459, 462, 465, 468, 471, 474, 477, 480, 483, 486, 489, 492, 495, 498 \][/tex]
This list provides all integers between 400 and 500 that are divisible by 3.
