Alright, let's work through 4903 times 8503 step by step
4903 × 8503 = 8503 × (4903)
+ 8503 × 3 giving us 25509
+ 8503 × 00 yielding 0
+ 8503 × 900 that equals 7652700
+ 8503 × 4000 producing 34012000

= 41690209
