## Thinking Mathematically (6th Edition)

(answers vary) An example of a four-digit number that is divisible by $4$ but not by $8$ is $1244$.
(Note that there are a number of possible answers to this item. RECALL: (1) A number is divisible by $4$ if the last two digits form a number that is divisible by $4$. (2) A number is divisible by $8$ if the last three digits form a number that is divisible by $8$. The divisibility rules above suggest that the a four digit number will be divisible by $4$ but not by $8$ if (a) the last two digits form a number that is divisible by $4$, but (b) the last three digits form a number that is not divisible by $8$. Notice that the four-digit number $1244$ has: (a) its last two digits form the number $44$ which is divisible by $4$ since $44\div 4 =11$; and (b) its last three digits form the number $244$ which is not divisible by $8$ since $244 \div 8 = 30.5$. Thus, an example of a four-digit number that is divisible by $4$ but not by $8$ is $1244$.