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Let$k$    be a field, and let${\mathcal{C}}$    be a$k$   -linear, Hom-finite triangulated category with split idempotents. In this paper, we show that under suitable circumstances, the Grothendieck group of${\mathcal{C}}$   , denoted by$K_{0}({\mathcal{C}})$   , can be expressed as a quotient of the split Grothendieck group of a higher cluster tilting subcategory of${\mathcal{C}}$   . The results we prove are higher versions of results on Grothendieck groups of triangulated categories by Xiao and Zhu and by Palu. Assume that$n\geqslant 2$    is an integer;${\mathcal{C}}$    has a Serre functor$\mathbb{S}$    and an$n$   -cluster tilting subcategory${\mathcal{T}}$    such that$\operatorname{Ind}{\mathcal{T}}$    is locally bounded. Then, for every indecomposable$M$    in${\mathcal{T}}$   , there is an Auslander–Reiten$(n+2)$   -angle in${\mathcal{T}}$    of the form$\mathbb{S}\unicode[STIX]{x1D6F4}^{-n}(M)\rightarrow T_{n-1}\rightarrow \cdots \rightarrow T_{0}\rightarrow M$    and$$\begin{eqnarray}K_{0}({\mathcal{C}})\cong K_{0}^{\text{sp}}({\mathcal{T}})\left/\left\langle -[M]+(-1)^{n}[\mathbb{S}\unicode[STIX]{x1D6F4}^{-n}(M)]+\left.\mathop{\sum }_{i=0}^{n-1}(-1)^{i}[T_{i}]\right|M\in \operatorname{Ind}{\mathcal{T}}\right\rangle .\right.\end{eqnarray}$$    Assume now that$d$    is a positive integer and${\mathcal{C}}$    has a$d$   -cluster tilting subcategory${\mathcal{S}}$    closed under$d$   -suspension. Then,${\mathcal{S}}$    is a so-called$(d+2)$   -angulated category whose Grothendieck group$K_{0}({\mathcal{S}})$    can be defined as a certain quotient of$K_{0}^{\text{sp}}({\mathcal{S}})$   . We will show$$\begin{eqnarray}K_{0}({\mathcal{C}})\cong K_{0}({\mathcal{S}}).\end{eqnarray}$$    Moreover, assume that$n=2d$   , that all the above assumptions hold, and that${\mathcal{T}}\subseteq {\mathcal{S}}$   . Then our results can be combined to express$K_{0}({\mathcal{S}})$    as a quotient of$K_{0}^{\text{sp}}({\mathcal{T}})$   .

GROTHENDIECK GROUPS OF TRIANGULATED CATEGORIES VIA CLUSTER TILTING SUBCATEGORIES