If 517*324 is divisible by 3, find the smallest digit that can replace .

Given data

• Number: 5,1,7,,3,2,4 (seven digits with unknown *)
• Divisibility target: by 3

Concept / Approach

• A number is divisible by 3 iff the sum of its digits is a multiple of 3.

Step-by-step calculation

Sum (excluding *): 5 + 1 + 7 + 3 + 2 + 4 = 22We need 22 + * ≡ 0 (mod 3) ⇒ * ≡ 2 (mod 3)Smallest digit satisfying this is 2.

Verification

22 + 2 = 24, which is divisible by 3.

Final Answer

2