+0  
 
+2
125
1
avatar+1227 

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+79894 
+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
Sort: 

1+0 Answers

 #1
avatar+79894 
+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

6 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details