Comparing 2013! and ${1007}^{2013}$

I have to compare the following two numbers:

$$2013!\text{and}{1007}^{2013}$$

where $n!=1\times 2\times \cdots \times (n-1)\times n$

I tried in different ways to group the $1\times 2\times \cdots \times 2012\times 2013$ to obtain some kind of association with the 1007 from ${1007}^{2013}$ but no luck.

Is there any standard approach for this kind of problem?

I have to compare the following two numbers:

$$2013!\text{and}{1007}^{2013}$$

where $n!=1\times 2\times \cdots \times (n-1)\times n$

I tried in different ways to group the $1\times 2\times \cdots \times 2012\times 2013$ to obtain some kind of association with the 1007 from ${1007}^{2013}$ but no luck.

Is there any standard approach for this kind of problem?