Question

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 $abcd dcba$

Answer 1

1111 is the greatest common divisor of all numbers.

Lets simplify the problem,

1234  +  4321   =   5555

2345  +  5432   =   7777

3456  +  6543   =   9999

4567  +  7654   =   12221

5678  +  8765   =   14443

6789  +  9876   =   16665

After it , we get:

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

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

Hence we get 1111 is the greatest common divisor.

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