2.5 Divisibility by 6

Rule: Number is divisible by both 2 and 3 (since 6 = 2×3 and 2, 3 are co-prime). Example: 3,924 → even (yes) and digit sum 3+9+2+4=18 (divisible by 3) → divisible by 6. Example: 4,562 → even (yes) but digit sum 4+5+6+2=17 (not div by 3) → NOT divisible by 6. Example (missing-value type): What least number must be added to 1,000 so that the sum is divisible by 6? 1000 ÷ 6 = 166 remainder 4 (since 6×166=996). To reach the next multiple of 6 (6×167=1002), we need 1002-1000=2. Least number to add = 2.

Example 4: Is 7,536 divisible by 6? Even? Last digit 6 → yes. Digit sum = 7+5+3+6=21, divisible by 3 → yes. Since both conditions hold, 7,536 is divisible by 6 (7536÷6=1256 exact ✓).

Example 5 (edge case — smallest number of a given size): Find the smallest 4-digit number that is exactly divisible by 6. The smallest 4-digit number is 1000. 1000 ÷ 6 = 166 remainder 4 (since 6×166=996). The next multiple of 6 after 996 is 6×167=1002. Smallest 4-digit multiple of 6 = 1,002.