Converting a number [tex]N[/tex] from base 10 to any base [tex]b[/tex] is a matter of finding the largest powers of [tex]b[/tex] that [tex]N[/tex] contains. However many copies of this power of [tex]b[/tex] are needed is equal to the leading digit of [tex]N[/tex] in base [tex]b[/tex]. 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
[tex]23_{10}=27_8[/tex]
