Index companies have gotten good at developing factor indices to stand alongside their core benchmark products. STOXX has recently created a set of factor indices that increase the set of choices for investors. STOXX has also launched with Qontingo (using the Axioma factor risk model), a tool for index factor analysis (factor iQ). See STOXX.com.
Below are the factor breakdowns for the STOXX Global 1800 Value index and the STOXX Global 1800 Momentum index with the factor exposures versus the STOXX Global 1800 index benchmark. Both have high factor exposures associated with their name. In the case of the value index, there are high exposures for B/P and earnings yield, and for the momentum index, there is a high exposure to the momentum factor.
However, there are also exposures to other factors such as liquidity, dividend yield, and market sensitivity for value and liquidity and growth for momentum. There is no such thing as a pure factor exposure. There can be steps in construction to limit exposure to other factors but there will be some mix of other stuff. Investors should be aware of other factors that influence their expected factor exposures.