To divide 130 base 4 by 13 base 4, you can perform long division, just like you would in base 10. Here's how it works:
10
__________
13 | 130
First, determine how many times 13 can go into the leftmost digit of 130 (which is 1 in base 4). In base 4, 13 is greater than 1, so we move to the next digit, which is 3.
Now, consider 13 in base 4 (which is 7 in base 10):
7
__________
13 | 130
Now, determine how many times 13 (base 4) can go into 13 (base 4). It goes exactly once:
7
__________
13 | 130
13
Now, subtract the result (7 in base 4) from the original number (130 in base 4):
7
__________
13 | 130
- 13
__________
00
Since we've reached a remainder of 0, we can conclude that 130 base 4 divided by 13 base 4 equals 7 base 4.