Thread: division

If you divide a 5 digit number by a 2 digit number, how many digits will the remainder have?

It will have 2 digits but is there a practical way to solve that type of questions?

Hey kastamonu.

There is a way and its through logarithms.

The number of digits left over after dividing m into n digit will be ln(m/n) = ln(m) - ln(n) where ln(m) is the number of digits (in fractional form) and ln(n) is the number of digits for n (again in fractional form).

You can round the log results but that's the basic idea.

for example 59873 by 45,
Logarithm method is not a quick way. You have to look for the log table. I need a more quick way to get the answer in 1-2 minutes.

By definition, the remainder does not exceed the divisor, so it will have at most two digits.

Many Thanks.