Promise,

I am going to illustrate the procedure by dividing 2252 by 23 in base 7

Before I actually start the division I am going to calculate 1× 23₇, 2 × 23₇, 3× 23₇ 4× 23₇ 5× 23₇ and
6× 23₇ by repeated addition.

1 × 23₇ = 23₇
2 × 23₇ = 23₇ + 23₇ = 46₇
3 × 23₇ = 46₇ + 23₇ = 102₇

and so on. My resulting table is

1 × 23₇ = 23₇
2 × 23₇ = 46 ₇
3 × 23₇ = 102 ₇
4 × 23₇ = 125 ₇
5 × 23₇ = 151 ₇
6 × 23₇ = 204 ₇

Now I can start the division.

I can see from my multiplication that 23₇ divides 225₇ 6 times. Thus I get, after subtraction

Again using of the table I see that 23₇ divides 212₇ 6 times and thus

Hence 2252₇ divided by 23₇ is 66₇ with a remainder of 5₇ .

Penny