Question

What is the base 8 equivalent of 23 base 10?

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

$23_{10}=27_8$