2.11 Divisibility by 12

Rule: Divisible by both 4 and 3 (since 12=4×3, co-prime factors). Example 1: 3,924 → last two digits 24 (÷4=6, divisible by 4); digit sum 3+9+2+4=18 (divisible by 3) → divisible by 12. Example 2: 91,224 → last two digits 24 (divisible by 4 ✓); digit sum 9+1+2+2+4=18 (divisible by 3 ✓) → divisible by 12. (Check: 91224 ÷ 12 = 7602 exact.)

Example 3: Is 47,916 divisible by 12? Last two digits = 16, 16÷4=4 exact → divisible by 4 ✓. Digit sum =4+7+9+1+6=27, divisible by 3 ✓. Since both hold, 47,916 is divisible by 12 (47916÷12=3993 exact ✓).

Example 4: Is 84,132 divisible by 12? Last two digits = 32, 32÷4=8 exact ✓. Digit sum =8+4+1+3+2=18, divisible by 3 ✓. Divisible by 12 (84132÷12=7011 exact ✓).