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No. For instance, 101 is not divisible by 11.

Q: Are all palindromic numbers divisible by 11?

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12

8 of the numbers less than 660 are divisible by 5 and 11 but not 3. All numbers divisible by 5 and 11 are multiples of their lcm; lcm(5, 11) = 55 All numbers divisibile by 5, 11 and 3 are multiples of their lcm; lcm(5, 11, 3) = 165 659 ÷ 55 = 11 54/55 → 11 numbers less than 660 are divisible by 5 and 11 659 ÷ 165 = 3 164/165 → 3 numbers less than 660 are divisible by 5, 11 and 3 → of the 11 numbers less than 660 divisible by 5 and 11, 3 are also divisible by 3 → 11 - 3 = 8 numbers less than 660 are divisible by 5 and 11 but not 3,.

Since all the numbers in that range start with "11", there is really only one option!

19

There are 9 palindromic numbers between 0 and 100: 11, 22, 33, 44, 55, 66, 77, 88 and 99.

Related questions

Yes, there are many palindromic numbers that are not evenly divisible by 11 such as 181, 232, 454, 585, 10001, 17871, etc.

All of them are divisible by 1.

11

11

All odd numbers are not evenly divisible by 7. Try 11, for example.

-11

12

8 of the numbers less than 660 are divisible by 5 and 11 but not 3. All numbers divisible by 5 and 11 are multiples of their lcm; lcm(5, 11) = 55 All numbers divisibile by 5, 11 and 3 are multiples of their lcm; lcm(5, 11, 3) = 165 659 ÷ 55 = 11 54/55 → 11 numbers less than 660 are divisible by 5 and 11 659 ÷ 165 = 3 164/165 → 3 numbers less than 660 are divisible by 5, 11 and 3 → of the 11 numbers less than 660 divisible by 5 and 11, 3 are also divisible by 3 → 11 - 3 = 8 numbers less than 660 are divisible by 5 and 11 but not 3,.

Since all the numbers in that range start with "11", there is really only one option!

19

88 and all its multiples

There are 9 palindromic numbers between 0 and 100: 11, 22, 33, 44, 55, 66, 77, 88 and 99.