The smallest 3-digit number divisible by 8 is 104.
Here's how we find it:
Understanding Divisibility
First, it's important to know what divisibility means. A number is divisible by another if the result of the division is a whole number with no remainder.
Finding the Smallest 3-Digit Number
The smallest 3-digit number is 100. Now, we need to find the smallest number greater than or equal to 100 that is divisible by 8.
Method to Find the Solution
- Start with the Smallest 3-Digit Number: Begin with 100, the smallest 3-digit number.
- Divide by 8: Divide 100 by 8. This gives us 12 with a remainder of 4 (100 / 8 = 12 R 4).
- Find the Difference: Calculate the difference between the divisor (8) and the remainder (4). This difference is 8 - 4 = 4.
- Add the Difference: Add the difference (4) to the smallest 3 digit number, which is 100. This gives us 100 + 4 = 104
- Verify: Check if 104 is divisible by 8: 104 / 8 = 13, with no remainder. So, 104 is divisible by 8.
Reference Note
While the provided reference deals with finding numbers divisible by multiple numbers (using the Least Common Multiple or LCM), the principle of using the remainder when dividing the smallest number to find the nearest divisible one is relevant. In our simple case, we're only focused on divisibility by 8. The reference states, "Now we will divide the smallest-3 digit number with the LCM obtained, and the remainder will be subtracted from the dividend, and 24 will be added to it to make it perfectly divisible." Though we are not using LCM here, the general principle of working with remainders applies. In our case we subtract the remainder from the divisor and add the result to the dividend, which is the smallest 3 digit number, to make it perfectly divisible.
Conclusion
Therefore, the smallest 3-digit number divisible by 8 is 104.
