In doing math calculations, it is sometimes very useful to remember some divisibility rules so you can quickly determine if a relatively large number is divisible by another number. Below is a list of the common divisibility rules:
· Divisible by 1: Any integer (not a fraction) is divisible by 1
· Divisible by 2: If the last digit is even: 0,2,4,6,8. For example, 128 is but 129 is not
· Divisible by 3: If the sum of the digits is divisible by 3. For example, 99996, with sum of digits 9+9+9+9+6=42. This rule can be repeated if needed.
· Divisible by 4: If the last 2 digits are divisible by 4. For example, the last 2 digits of 1420 is 20, which is divisible by 4.
· Divisible by 5: If the last digit is 0 or 5. For example, 185 is but 842 is not.
· Divisible by 6: If the number is even and is divisible by 3. For example, 9996 is both even and divisible by 3.
· Divisible by 7: If the double of the last digit subtracted from the number formed by the remaining digits is divisible by 7. For example, in number 105, double 5 we get 10, subtract it from the remaining number, 10, and we get 0, which is divisible by 7. So 105 is divisible by 7. This rule can be repeated if needed.
· Divisible by 8: If the last 3 digits are divisible by 8. For example, 209816's last 3 digits are 816, which is divisible by 8. So 209816 is divisible by 8.
· Divisible by 9: If the sum of the digits is divisible by 9. For example, sum of the digits of 1629 is 18, which is divisible by 9, so 1629 is divisible by 9. This rule can be repeated if needed.
· Divisible by 10: If the number ends in 0. For example, 890, 2000, etc.
· Divisible by 11: If you add and subtract the digits alternatingly, and the result is divisible by 11. For example, 1364: +1-3+6-4=0, divisible by 11, so the number 1364 is divisible by 11.
· Divisible by 12: If the number is divisible both by 3 and by 4. For example, number 648 is divisible both by 3 and 4, so it is divisible by 12.