Divisibility rules (other)

Other divisibility rules

Combining rules for small divisors gives quick tests for other numbers:

• Divisible by $6$ iff divisible by $2$ and by $3$ (last digit even and digit sum divisible by $3$).
• Divisible by $12$ iff divisible by $3$ and by $4$ (digit sum divisible by $3$, last two digits divisible by $4$).
• Divisible by $8$ iff the number formed by the last three digits is divisible by $8$ (same idea as the rule for $4$: $10^3 = 8 \cdot 125$).

Examples

• $2\,136$ is divisible by $8$ because the last three digits form $136 = 8 \times 17$.
• $2\,340$ is divisible by $12$: digit sum $2+3+4+0 = 9$ (divisible by $3$), and last two digits $40$ are divisible by $4$.