+0  
 
+1
488
5
avatar+141 

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+8966 
+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+141 
+1

That's incorrect, sorry.

 Jun 13, 2019
 #3
avatar+8966 
+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+111438 
+4

Nice, hectictar   !!!!

 

cool cool cool

CPhill  Jun 13, 2019
 #5
avatar+141 
+2

Thanks so much!

 Jun 13, 2019

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