When can a k-form be expressed as a wedge product of one forms?

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Suppose I am handed a k-form $\omega$. What can I do to check if $\omega$ can be expressed in the form

$$\omega = \alpha_1 \wedge \dots \wedge \alpha_k?$$

The context for this question is an application in differential geometry. A codimension-k surface is characterized by a k-form field of the above form; I am trying to ascertain when a specified k-form field defines a codimension-k surface

EDIT: An equivalent question is, "when is a given k-form the unique top-level form of some k-dimensional subspace?"