What is the Big O ( time complexity ) for factorial computations?

It is linear for the iterative version:

// O(n)
function factorial (n) {
  let ret = 1;
  for(let i = 2; i <= n; i++) {
    ret = ret * i;
  }
  return ret;
}

and it appears to be linear for the recursive version as well:

function factorialR (n) {
  if( n === 0 || n === 1 ) {
    return 1;
  } else {
    return n * factorialR(n - 1);
  }
}

Is it linear for the recursive version as well? Instead of a loop for each additional value it is just an additional function call.