Mathematics question

Question

1125899906842624 mod 13

What is the fastest way to find for the answer?

Answer 1

multiply last digit by 4

add it to the other numbers

repeat, repeat, repeat, ...

1258999068426241

16

112589990684278

32

11258999068459

36

11258999068495

25

1125899906874

16

112589990703

12

112589990782

8

11258999086

24

11258999110

1125899911

4

1125899915

20

1125899935

25

1125899960

112589996

24

112590120

11259012

8

1125909

36

112626

24

11284

16

1144

16

130

13 is divisible by 13 so the original number is too

or just use a calculator = 8.6676851 x 10^12 which means no remainder

or long division

calculator is fastest