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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?

tertre  Mar 19, 2017

Best Answer 

 #1
avatar+87293 
+2

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

 

 

cool cool cool

CPhill  Mar 19, 2017
 #1
avatar+87293 
+2
Best Answer

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

 

 

cool cool cool

CPhill  Mar 19, 2017

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