A number theory problem by vishwathiga jayasankar

We have,

$764 = \color{#D61F06}{2} \cdot 7^3 + \color{#D61F06}{1} \cdot 7^2 + \color{#D61F06}{4} \cdot 7^1 + \color{#D61F06}{1} \cdot 7^0$

Therefore ${\left( 764 \right)}_7 = \boxed{2141}$ .