Question

A palindromic number is a number that reads the same when the order of its digits is reversed.

What is the difference between the largest and smallest five-digit palindromic numbers that
are both multiples of 45?

Answer 1

Explanation:

A five-digit palindromic number is a number that has 5 digits and is the same when read forwards and backwards. A multiple of 45 is a number that is divisible by 45.

To find the largest five-digit palindromic number that is a multiple of 45, we need to find the largest five-digit palindrome and then find the largest multiple of 45 that is less than or equal to that palindrome.

The largest five-digit palindrome is 99999. The largest multiple of 45 less than or equal to 99999 is 99945.

To find the smallest five-digit palindromic number that is a multiple of 45, we need to find the smallest five-digit palindrome and then find the smallest multiple of 45 that is greater than or equal to that palindrome.

The smallest five-digit palindrome is 10001. The smallest multiple of 45 greater than or equal to 10001 is 10035.

To find the difference between the largest and smallest five-digit palindromic numbers that are both multiples of 45, we can subtract the smallest from the largest:

99945 - 10035 = 8910

So the difference between the largest and smallest five-digit palindromic numbers that are both multiples of 45 is 8910.