```typescript
/**
 * The factorial of n.
 */
export function factorial(n: number): number {
  if (typeof n !== 'number' || isNaN(n) || !Number.isInteger(n)) {
    throw new Error('Invalid argument: must be a non-negative integer.');
  }
  if (n < 0) {
    throw new Error('Factorial is not defined for negative numbers.');
  }
  if (n === 1) {
    return 1;
  }
  return n * factorial(n - 1);
}
```