6: The integer must end in either a 0, 2, 4, 6, or 8, and the sum of its digits is divisible by 3. (Example. 24. Ends in a 4, and sum of digits (2+4 = 6) is divisible by 3)
7: To determine if the number 672 is divisible by 7, start by multiplying the last digit by 2, which in this case results in 4. Subtracting this from the rest of the number, 67 minus 4, yields 63. Since 63 can be divided by 7 evenly to result in 9, it is simple to conclude that 672 is divisible by 7.
8:
A number is divisible by 8 if the number formed by its last three digits is divisible by 8. 3240 is divisible by 8, because 240 is divisible by 8. 3145 is not divisible by 8, because 145 is not divisible by 8.
9: This is similar to the rule for 3. A number is divisible by 9 if the sum of its digits is divisible by 9. 7065 is divisible by 9, because 7 + 0 + 6 + 5 = 18 which is divisible by 9. 3045 is therefore not divisible by 9, because 12 is not divisible by 9.
