As Guambra Feo has pointed out, metaphysical presupposition play a role in determining an answer. For instance, the term 'noumenon' invokes the term 'real' or 'objective' indirectly by referencing 'sense-independence'. From WP:
In philosophy, a noumenon (/ˈnuːmənɒn/, /ˈnaʊ-/; from Ancient Greek νoούμενον; PL: noumena) is knowledge posited as an object that exists independently of human sense.
So, one's ontological commitments must be made manifest before an answer can be given. A mathematical realist would be in the position of answering yes. If numbers are somehow real as Platonic forms or otherwise, then there would be noumenal aspect to them, as they exist independently of human cognition and sense. For a mathematical fictionalist as in Hartry, numbers have no noumenal aspect as they are entirely phenomenological in the sense that they are a function of cognition and are not independent at all of cognition.
Thus, you wind up at the great obviator of philosophical discourse, "it depends".