Summary: Using the [the second author et al., Acta Math. 218, No. 1, 55–135 (2017; Zbl 1409.14053)] construction, we give a simple proof for the fact that the Euler characteristic of a hyper-Kähler manifold of OG10 type is \(\chi(\mathrm{OG}10)=176, 904\), a result previously established by S. Mozgovoy [The Euler number of O’Gradys 10-dimensional symplectic manifold. Mainz: Johannes Gutenberg-Universität (PhD Thesis) (2007)].