What least number must be added to 1056 so that the sum is exactly divisible by 23?

Given data

• Target: smallest k ≥ 0 with (1056 + k) divisible by 23.

Concept / Approach

• Compute 1056 mod 23; add the complement to the next multiple.

Step-by-step calculation

23 × 45 = 1,035Remainder r = 1,056 − 1,035 = 21Need k = 23 − r = 2 ⇒ 1,056 + 2 = 1,058 = 23 × 46Thus, k = 2

Common pitfalls

• Choosing remainder itself instead of the complement to reach the next multiple.

Final Answer

2