The conversion factor always has a value of 1. It is a fraction with the numerator equal to the denominator -- only the units are different.
The numerator units are the units you're converting <u>to</u>: millimeters. The denominator units are the units you're converting <u>from</u>: centimeters.
You know that 1 cm = 10 mm, so when you arrange the fraction as described, the conversion factor you're multiplying by is ...