Check which answer choice does not divide $72$ evenly:

• $72 \div 3 = 24$ $\checkmark$
• $72 \div 4 = 18$ $\checkmark$
• $72 \div 8 = 9$ $\checkmark$
• $72 \div 16 = 4.5$ $\boldsymbol{\times}$
• $72 \div 24 = 3$ $\checkmark$

Since $72 \div 16 = 4.5$, which is not a whole number, $16$ does not divide evenly into $72$.