Question

Smallest 7 digit palindrome divisible by 15 and largest

Answer 1

We can write 7 digit palindrome number as:

a b c d c b a

And because it is divisible by 15, it have to be divisible by 5 and 3 ( 5 * 3 = 15 ).

The last number a = 0, or 5. But it is not 0, because the first digit can`t be 0.

So:  a =5

This number becomes:  5 b c d c b 5.

The smallest palindrome number is: 5002005 ( b = c = 0 )

Because 5 + 0 + 0 + 2 + 0 + 0 + 5 = 12 ( divisible by 3 )

The largest palindrome number is: 5998995   ( b = c = 9 )

Because 5 + 9 + 9 + 8 + 9 + 9 + 5 = 54  ( divisible by 3 ).

Answer: The smallest number is 5002005 and the largest number is 5998995.