We want to calculate 1664/65.
We can do this step by step. First, from the original number, we will add digit by digit until we have a number that is greater than 65.
So at first, we have number 1. This number is not greater than 65 so we add the 6.
We get the number 16, which is again less than 65. So we add the other 6.
We get the number 166 which is greater than 65. Now, we want to calculate the maximum number to which we can multiply 65 such that the product is less than 166.
Note that 1*65 = 65,
2 * 65 = 130
3*65 = 195 which is greater than 166. So in this case we keep the number 2 in mind.
NOw, to proceed, we multiply 65 times 2 and then subtract this to 166.
So we get
166 - 2*65 = 166 -130 = 36.
This number is less than 65, so we add the number 4 we had.
We get the number 364. Since it is greater than 65. We do as before: we want to find the maximum number to which we multiply 65 and we get a number that is less than 364.
Note that
65 * 5 = 325
65*6 = 390 which is greater that 364. So the number we are looking for is 5.
We had 2 already from the previous step . So we add the 5 to the 2 to get 25.
Now, we subtract 325 to 364
364 -325 = 39
since 39 is less than 65 and there are no more numbers to add, we stop and we say that 1664/65 is 25 with a residue of 39 . This means that
1665 = 25*65 + 39