Here's a simple method:

since the product of the two numbers is 436,995 (which ends with 5), one of the two numbers should end with 5.And since it is a palindrome, it should also begin with 5. So, this number is is ;where a can be any number from 0 to 9.

Now you can divide the number 436,995 by 5a5 till the result get a palindrome..

436,995/505= 865.33

436,995/515=848.53

436,995/525=832.37

436,995/535=816.81

436,995/545=801.82

436,995/555=787.37

436,995/565=773.44

436,995/575=759.99

436,995/585=747...There you go!