Divisibility rules for 5 and 10

Divisibility by 5

A number is divisible by $5$ iff its last digit is $0$ or $5$.

Divisibility by 10

A number is divisible by $10$ iff its last digit is $0$.

Both rules follow from the fact that $10 = 2 \cdot 5$, so in base 10 only the last digit contributes to the remainder modulo $5$ or $10$.

Examples

• $12\,345$ is divisible by $5$ (last digit $5$).
• $8\,120$ is divisible by $10$ (last digit $0$), and therefore also by $5$.