To factor the expression \(28q - 49r\), we first need to find the greatest common factor (GCF) of the two terms.
The coefficients are 28 and 49. The GCF of 28 and 49 is 7.
Now, we can factor out the GCF:
\[ 28q - 49r = 7(4q - 7r) \]
Thus, the expression \(28q - 49r\) factored as a product with a whole number greater than 1 is:
\[ \boxed{7(4q - 7r)} \]