We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
102
5
avatar+140 

The four consecutive digits a, b, c and d are used to form the four-digit numbers abcd and dcba. What is the greatest common divisor of all numbers of the form abcd+dcba?

 Jun 12, 2019

Best Answer 

 #3
avatar+8579 
+4

1234  +  4321   =   5555

2345  +  5432   =   7777

3456  +  6543   =   9999

4567  +  7654   =   12221

5678  +  8765   =   14443

6789  +  9876   =   16665

 

And....

 

5555 _=_ 101 * 11  * 5
7777 = 101 * 11 * 7
9999 = 101 * 11 * 3 * 3
12221 = 101 * 11 * 11
14443 = 101 * 11 * 13
16665 = 101 * 11 * 3 * 5

 

gcd(5555, 7777, 9999, 12221, 14443, 16665)  =  101 * 11  =  1111

 Jun 13, 2019
 #1
avatar
-3

The greatest GCD of abcd and dcba is when they total 9999 when added together. So:

3456 and 6543 have a GCD of 9.

 Jun 13, 2019
 #2
avatar+140 
+1

That's incorrect, sorry.

 Jun 13, 2019
 #3
avatar+8579 
+4
Best Answer

1234  +  4321   =   5555

2345  +  5432   =   7777

3456  +  6543   =   9999

4567  +  7654   =   12221

5678  +  8765   =   14443

6789  +  9876   =   16665

 

And....

 

5555 _=_ 101 * 11  * 5
7777 = 101 * 11 * 7
9999 = 101 * 11 * 3 * 3
12221 = 101 * 11 * 11
14443 = 101 * 11 * 13
16665 = 101 * 11 * 3 * 5

 

gcd(5555, 7777, 9999, 12221, 14443, 16665)  =  101 * 11  =  1111

hectictar Jun 13, 2019
 #4
avatar+102415 
+4

Nice, hectictar   !!!!

 

cool cool cool

CPhill  Jun 13, 2019
 #5
avatar+140 
+2

Thanks so much!

 Jun 13, 2019

15 Online Users

avatar