Explanations:To find the largest 3-digit number that is completely divisible by 7, we need to understand the concept of divisibility and how to apply it to a specific range of numbers. The largest 3-digit number is 999. We need to find the largest number less than or equal to 999 that is divisible by 7.
The process involves dividing 999 by 7 and then finding the largest multiple of 7 that is less than or equal to 999. We can perform the division as follows:
999 ÷ 7 = 142.7142857...
Since we are looking for a whole number, we take the integer part of the quotient, which is 142. This means that 142 is the largest integer such that 142 × 7 is less than or equal to 999. We can calculate this product:
142 × 7 = 994
Thus, 994 is the largest 3-digit number that is completely divisible by 7. We can verify this by checking the divisibility of 994 by 7:
994 ÷ 7 = 142
Since 994 divided by 7 gives an integer quotient of 142 with no remainder, 994 is indeed divisible by 7. Therefore, the correct answer is 994.
It is important to note that the other options (991, 992, and 993) are not divisible by 7. We can check their divisibility by performing the division:
991 ÷ 7 = 141.57142857...
992 ÷ 7 = 141.71428571...
993 ÷ 7 = 141.85714285...
Each of these divisions leaves a remainder, confirming that 991, 992, and 993 are not divisible by 7.
In summary, the largest 3-digit number that is completely divisible by 7 is 994. This is determined by finding the largest multiple of 7 that is less than or equal to 999, which is 994.