Find the largest positive integer that leaves the same remainder when divided into each of 889, 961, 1009, and 1189

Answer 1

889/12 = 74 with remainder 1
961/12 = 80 with remainder 1
1009/12 = 84 with remainder 1
1189/12 = 99 with remainder of 1

So 12 is it!

I am not sure if you know anything about modular arithmetic, so I made up a silly little old-fashioned computer program.
Here is a listing of it, with the output at the end.
The first column of the output is the remainder, the second number is the largest positive integer.
It found none larger than 12

10 for n = 2 to 889
20 r1 = 889-int(889/n)*n
30 r2 = 961-int(961/n)*n
40 if r1 = r2 then 50 else goto 100
50 r3 = 1009-int(1009/n)*n
60 if r3 = r2 then 70 else goto 100
70 r4 = 1189-int(1189/n)*n
80 if r4 = r3 then 90 else goto 100
90 print r4,n
100 next n
>run
1 2
1 3
1 4
1 6
1 12

I did this with something called "Chipmunk Basic"