What is the smallest number to add to 4456 so the sum is divisible by 6?

Given data

• We want the least k ≥ 0 such that 4456 + k is divisible by 6.

Concept / Approach

• Divisible by 6 ⇔ divisible by 2 and 3.
• 4456 is even ⇒ divisible by 2 already; adjust k to satisfy divisibility by 3.

Step-by-step calculation

Digit sum of 4456 = 4 + 4 + 5 + 6 = 19We require 19 + k ≡ 0 (mod 3)Next multiple of 3 after 19 is 21 ⇒ k = 2Check parity: 4456 + 2 = 4458 (even). Both conditions met.Therefore, k = 2.

Verification

4458 ÷ 6 = 743 exactly.

Common pitfalls

• Making the sum divisible by 3 but turning it odd; verify both divisibility-by-2 and by-3.

Final Answer

2