There are eight 3-digit palindromes divisible by 11.
Understanding Palindromes and Divisibility by 11
A palindrome is a number that remains the same when its digits are reversed. A three-digit palindrome has the form ABA, where A and B are digits from 0 to 9, and A cannot be 0. Divisibility by 11 means that the number is perfectly divisible by 11 without leaving a remainder.
While not all palindromes are divisible by 11, there's a pattern for those with an even number of digits: they are always divisible by 11. However, this rule doesn't apply to palindromes with an odd number of digits, like our three-digit case.
Finding the 3-Digit Palindromes Divisible by 11
Let's list them:
- 121
- 242
- 363
- 484
- 616
- 737
- 858
- 979
These are all the three-digit palindromes that are divisible by 11. You can verify this by performing the division for each number.
A Note on Other Digit Palindromes
It's important to note that the divisibility rule by 11 changes based on the number of digits. For example:
- Even-digit palindromes: Always divisible by 11.
- Odd-digit palindromes: Not always divisible by 11; the divisibility depends on the specific digits.
This information clarifies why there are only eight three-digit palindromes fitting our criteria.
