To decide whether a number of n digits is divisible by 7, we can define a process by which its
magnitude is reduced as follows: (i1
, i2
, i3…..in are the digits of the number, starting from the
most significant digit).
i1
i2…in
fi i1
. 3
n–1 + i2, 3
n–2 + …. + In3
0
.
e.g. 259 fi 2.3
2 + 5.3
1 + 9.3
0 = 18 + 15 + 9 = 42
Ultimately the resulting number will be seven after repeating the above process a certain number
of times.
After how many such stages, does the number 203 reduce to 7?