An eight-digit integer is formed by repeating a positive four-digit integer. For example, 25,632,563 or 60,786,078 are integers of this form. What is the greatest common divisor of all eight-digit integers of this form?

Note....any number of the form abcdabcd can be written as

abcd * 10000 + abcd =

adcd ( 10000 + 1) =

abcd (10001)

So.....10001 is the greatest common divisor for any number of this form