To increase the frequency by 4 octave (s), to 16f0, by what factor would you have to decrease the length?

= 16, length will be decreased by a factor of 16

Explanation:

One octave apart corresponds to twice the frequency and thus half the length. Two octaves apart will correspond to 4 times the frequency and the length will be reduced by a factor of 4, that is 1/4 of the length. Three octaves apart on the other hand corresponds to 8 times the frequency, thus length will be decreased by a factor of of 8, that is 1/8 of the length. Four octaves apart corresponds to 16 times the frequency, therefore the length will be decreased by a factor of 16, that is 1/16 of the length.