# Exploring properties of palindromic numbers

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## Lesson details

### Key learning points

- In this lesson we explore conjectures involving palindromic numbers and multiples of 11.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

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### 5 Questions

Q1.

Which of the following statements are true?

Any number with the digit 7 is a palindromic number

Any number with the digit 8 is a palindromic number

Any two digit number is a palindromic number

Q2.

Which of the numbers below are not palindromic?

14

231

3

Q3.

Which of the numbers below requires more than 2 iterations?

47

53

81

Q4.

How many iterations does the number 173 require?

1

3

4

Q5.

How many iterations does the number 89 require?

3

6

9

### 5 Questions

Q1.

Which of the following numbers is not a multiple of 11?

11

110

44

Q2.

Which of the following statements is not correct?

Some palindromic numbers are even

Some palindromic numbers are multiples of 11

Some palindromic numbers are odd

Q3.

Which of the following conjectures is true?

All palindromic numbers are divisible by 11

All palindromic numbers larger than 1000 are divisible by 11.

Palindromic numbers with an odd number of digits are divisible by 11.

Q4.

Which of the 3 digit palindromic numbers below is divisible by 11?

132

454

666

Q5.

Which of the numbers below are divisible by 11

22422

4

545