Problem dealing with some Number Theory "multiple of some #"

My Question about this problem:

They say, 100 is a multiple of 4, so that's why the units digit of 3100 is the same as that of 34 However, 100 is also a multiple of 5. So why did they pick 4?

Please help explain this--as I am not hot in number theory

If *n* is an integer with units digit 3,

what is the units digit of *n* 100 ?

Since only the units digit of *n* matters, you can start by exploring what happens when *n* equals 3. Raise 3 to powers and observe the units digits of the results.

31 = 3

32 = 9

33 = 27

34 = 81

35 = 243 3

9

7

1

3 Notice that the units digit of 35 is again 3, so from here on the sequence will repeat itself and continue to cycle through the four values 3, 9, 7, 1. Since 100 is a multiple of 4, the units digit of 3100 is the same as that of 34