We have to find the remainder of [tex] \frac{29107}{37} [/tex].
Now, 29017 can be written as
[tex] 29107-800*37+800*37=29107-29600+800*37\\
=-493+800*37\\
=-493+(800-13+13)*37\\
=-493+(787+13)*37\\
=-493+13*37+787*37\\
=-493+481+787*37\\
=-12+787*37\\
=-12+37+786*37\\
=786*37+25 [/tex]
Thus 29107=786*37+25.
The remainder when 29107 is divided by 37 is [tex] 25 [/tex].
