#### Answer

The number is $34$.

#### Work Step by Step

Let
$x$ = the unknown number
Then
"the product of 8 and a number" means $8(x)$.
Thus, the equation that represents the situation is:
$8(x)=272$
Divide 8 on both sides of the equation to obtain:
$x=\frac{272}{8}
\\x=34$