Question

What is the base 8 equivalent of 23 base 10?

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Answer 1

Converting a number
`N` from base 10 to any base
`b` is a matter of finding the largest powers of
`b` that
`N` contains. However many copies of this power of
`b` are needed is equal to the leading digit of
`N` in base
`b`. Then keep doing this with the remainder terms as needed.

In this case,

23 = 16 + 7 = 2*8^1 + 7

so the first digit of 23 in base 8 is 2. The remainder 7 contains no powers of 8, so we're done; the last digit is this remainder, and we write

`23_(10)=27_8`