Alright, let's work through 7263 times 8744 step by step
7263 × 8744 = 8744 × (7263)
+ 8744 × 3 resulting in 26232
+ 8744 × 60 producing 524640
+ 8744 × 200 producing 1748800
+ 8744 × 7000 that is equal 61208000

= 63507672
