Explanation: To find the largest 3-digit number completely divisible by 7, we start by identifying the largest 3-digit number, which is 999. We then need to determine the largest multiple of 7 that is less than or equal to 999.
First, we perform the division of 999 by 7:
\[ 999 \div 7 = 142.7142857 \]
The quotient is 142 and the remainder is 5. This means that 999 is not completely divisible by 7, as there is a remainder of 5.
To find the largest multiple of 7 that is less than or equal to 999, we take the quotient 142 and multiply it by 7:
\[ 142 \times 7 = 994 \]
This means that 994 is the largest 3-digit number that is completely divisible by 7.
To verify, we can perform the division of 994 by 7:
\[ 994 \div 7 = 142 \]
The quotient is 142 and the remainder is 0, confirming that 994 is completely divisible by 7.
Therefore, the largest 3-digit number completely divisible by 7 is 994.
This problem involves understanding the concept of division and remainders, and how to find the largest multiple of a given number within a specified range. It is a fundamental concept in number theory and arithmetic, often tested in various competitive examinations.