Cholesky[A_]:=(
n=Length[A];
L=Table[0,{i,n},{j,n}];
For[k=1, k≤n, k++, (*Iterate over the columns*) 
(*Find the diagonal element*)
L[[k,k]]=(Sqrt[A[[k,k]]-Sum[L[[k,p]]^2,{p,1,k-1}]]);
For[j=k+1,j≤n,j++, (*Find all the elements below the main diagonal*)
L[[j,k]]=((A[[k,j]]-Sum[L[[k,i]]L[[j,i]],{i,1,k-1}])/(L[[k,k]]))
]
];
L
)

Cholesky[{{10,45,285},{45,285,2025},{285,2025,15333}}]