Question 1116259: A palindrome number is a number that is the same when it’s digits are reversed. Find the largest palindrome number that is the product of two 2-digit numbers?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website!  , so a product of two two-digit numbers is at most  ,
and a palindrome that is a product of two two-digit numbers is less than .
The largest palindrome that is less than is  .
If the first two digits are  and  in that order,
the number's digit read like  ,
and the number is a multiple of  ,
because its value is
 .
If that  factor can be further factored as
a two-digit number  times a single digit number  ,
the palindrome can be factored as the product of the two-digit numbers  and :
For example, , with  can be factored as
 ,
and does not work.
If we try all possible values for  , we find
 .
Out of all those values for  ,
none is divisible by  , or  , or  ,
and only two of them are divisible by  .
That rules out all possible digit factors except and  , is divisible by  .
So, with  ,
is a palindrome that can be written as a product of two two-digit numbers.
There will be others, such as  ,
but  is the largest palindrome number that is the product of two 2-digit numbers.
|
|
|
