The smallest number divisible by 11 is 11.
Here's why:
- Definition of Divisibility: A number is divisible by another number if it can be divided by that number with no remainder.
- Starting Point: We start with the smallest positive integer, which is 1. 1 is not divisible by 11 because 1 divided by 11 is 0 with a remainder of 1. 2 is not divisible by 11 for similar reasons. We continue until we reach 11.
- The Number 11: When 11 is divided by 11, the result is 1 with no remainder. This is why 11 is divisible by 11.
Divisibility Rule of 11
Although not directly needed to determine the smallest number divisible by 11, it's helpful to know the divisibility rule for 11, which is used for larger numbers:
- Sum the digits in the odd positions (from the right).
- Sum the digits in the even positions (from the right).
- If the difference between the two sums is 0 or divisible by 11, then the number is divisible by 11.
4-Digit Numbers Divisible by 11
The reference provided states: 1001 is the smallest and 9999 is the largest 4-digit number divisible by 11. Although not directly related to finding the smallest number divisible by 11, this is a useful example of applying the divisibility rule for larger numbers:
- Example 1: 1001 - (1 + 0) - (0 + 1) = 0. Therefore, 1001 is divisible by 11.
- Example 2: 9999 - (9 + 9) - (9 + 9) = 0. Therefore, 9999 is divisible by 11.
| Number | Divisible by 11 |
|---|---|
| 1 | No |
| 2 | No |
| 3 | No |
| ... | ... |
| 10 | No |
| 11 | Yes |
| 22 | Yes |
