The gravitational force between two objects is given by Newton's law of universal gravitation:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between their centers.
If the distance \( r \) is decreased by half, the new distance is:
\[ r' = \frac{r}{2} \]
The new gravitational force \( F' \) can be calculated as:
\[ F' = \frac{G \cdot m_1 \cdot m_2}{(r/2)^2} = \frac{G \cdot m_1 \cdot m_2}{\frac{r^2}{4}} = 4 \cdot \frac{G \cdot m_1 \cdot m_2}{r^2} = 4F \]
This shows that the gravitational force increases by a factor of 4 when the distance is halved.
Thus, the answer is 4.