If 481*673 is divisible by 9, find the smallest digit that can replace

Given data

• Number: 481673
• Divisibility requirement: by 9

Concept / Approach

• A number is divisible by 9 if the sum of its digits is a multiple of 9.

Step-by-step calculation

Sum of known digits = 4 + 8 + 1 + 6 + 7 + 3 = 29We need 29 + * ≡ 0 (mod 9) ⇒ 29 ≡ 2 (mod 9), so * ≡ 7 (mod 9)Smallest digit satisfying this is 7

Verification

29 + 7 = 36, a multiple of 9.

Common pitfalls

• Using divisibility by 3 instead of 9; both use digit sums but mod 9 is required here.

Final Answer

Smallest digit is 7.