The four consecutive digits $a$, $b$, $c$ and $d$ are used to form the four-digit numbers $abcd$ and $dcba$. What is the greates

Question

2 years ago

9

t common divisor of all numbers of the form $abcd dcba$

1 answer:

serg [7] · Answer 1 · 2023-06-09T13:40:46+03:00

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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